Past seminars & recordings
Past seminars & recordings
Click on an entry to see the abstract.
The vacua of specific non-semisimple, dyonic gaugings of maximal four-dimensional supergravity have recently attracted some interest because they consistently uplift to typically non-geometric S-fold solutions of type IIB supergravity. In contrast to other consistent uplifts, these vacua and their associated IIB S-folds tend to come in families parameterised by $D=4$ supergravity moduli. For this reason, gauged supergravity is an excellent starting point to assess holographically the conformal manifolds of the dual conformal field theories. In this talk, I will review recent progress in the holographic assessment of the spectrum of single-trace operators on this type of conformal manifolds, using new tools derived from exceptional field theory. As a by-product of our analysis, we will provide evidence of the non-compactness of some of these conformal manifolds. This observation appears to be in tension with one of the very many conjectures formulated in the context of the swampland programme.
24/06/2022
I will discuss generalisations of U-duality transformations which do not rely on the existence of isometries. First I will review a recently proposed generalised U-duality map between solutions of type IIA supergravity of the form M_7 x S^3, with NSNS flux, and solutions of 11-dimensional supergravity, in which the three-sphere is replaced by a four-dimensional geometry which encodes three-algebra structure constants (see my previous exceptional geometry seminar, from February, for a first look at this). I will show that when M_7 admits two abelian isometries, TsT deformations on the IIA side become six-vector deformations in the 11-dimensional setting. These six-vector deformations involve an action of E_6 on both isometric and non-isometric directions. I will discuss the algebraic interpretation of these deformations, and compare and contrast them with (generalised) Yang-Baxter deformations in supergravity.
17/06/2022
The doubled formulation of the worldsheet provides a description of string theory in which T-duality is promoted to a manifest symmetry. I will discuss the extension of doubled formulation to N=(2,2) superspace thus providing a doubled formulation for bi-Hermitian/generalised Kähler target spaces. The dynamics of a doubled model is concisely described by a single function, a doubled-generalised Kähler potential, supplemented with a manifestly N=(2,2) constraint. The developed formalism will be applied to concrete examples.
03/06/2022
We will review a recent application of Exceptional Field Theory : finding new families of solutions of type IIB supergravity on $AdS_4 \times S^1 \times S^5$. To find such solutions, we will compactify type IIB on $S^5 \times S^1$ to obtain a 4d gauged maximal supergravity where new solutions are simply found by extremizing a scalar potential. Surprisingly, it is sometime possible to deform our new solutions and break any residual supersymmetry while preserving stability. This is surprising since, from a holographic perspective, these deformations should be dual to non-supersymmetric exactly marginal deformations. We will show that it is a generic behaviour of gravity theories compactified on a circle and we will provide a solution generating technique in terms of a tool called the mapping torus.
20/05/2022
We consider the space of supersymmetric AdS5 solutions of type IIB supergravity corresponding to the conformal manifold of the dual 4d N = 1 conformal field theories. We describe how the background geometry naturally encodes a holomorphic generalised structure, dual to the superpotential of the field theory. Using this generalised language, we address the long-standing problem of finding the gravity duals of the generic N = 1 deformations of N = 4 super Yang-Mills: though we are not able to give it in a fully explicit form, we provide a proof-of-existence of the supergravity solutions. Using this formalism, we analyse the moduli of these supergravity backgrounds and derive a new result for the Hilbert series of the deformed field theories.
06/05/2022
We will present recent progress in the classification and construction of supersymmetric AdS(3) solutions in String Theory. This includes the classification of minimally supersymmetric solutions, and the construction of large families of N=(2,0) supersymmetric AdS(3) solutions in massive Type IIA supergravity. We will also discuss N=(2,2) supersymmetric AdS(3) solutions arising from D3-branes on Riemann surfaces of constant, as well as non-constant curvature.
22/04/2022
After a short introduction on conformal branes in WZW models I will discuss the study of integrable brane configurations embedded in lambda-deformations. Then, I will focus on integrable branes embedded in a class of models known as generalized lambda-deformations which appear as multi-parametric deformations of a product of WZW models and interpolate between two exact CFTs in the UV and IR fixed points.
08/04/2022
I will introduce exact expressions, manifestly covariant under Goddard-Nuyts-Olive duality, for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of N=4 SYM with classical gauge group. These correlators are found to satisfy intriguing "Laplace-difference equation" under the action of the hyperbolic Laplace operator with respect to the complex YM coupling. The perturbation expansions of these integrated correlators for any finite value of N agree with properties obtained from perturbative Yang--Mills quantum field theory. In the large-N limit these correlators make contact with the low energy expansion of type IIB superstring theory in an AdS_5×S^5/Z_2 background.
01/04/2022
D-branes will be introduced in the framework of doubled geometry as conformal boundary conditions for the open string formulation of the Born sigma-model. This suggests a general characterisation of such D-branes as maximally isotropic subbundles on a para-Hermitian manifold. In particular, the reduction procedure of the D-branes to the physical spacetime will be tackled by describing them as Dirac structures. Furthermore a comparison with generalised complex branes will be drawn by defining their para-complex counterpart.
18/03/2022
The double copy construction in scattering amplitudes hints at a deep connection between Yang-Mills (YM) theory and gravity. It states, roughly speaking, that exchanging the colour information by the kinematic information of gluon scattering amplitudes leads to gravity amplitudes. A first principle understanding of this colour-kinematic double copy, however, remains elusive. The main objective of this talk is to show that Double Field Theory (DFT) is a promising framework to understand the double copy. I will start the talk with a discussion of a colour-kinematic substitution at the level of the YM action. This substitution is based on scattering amplitudes, and reproduces the gauge invariant DFT action to quadratic order, and a gauge fixed DFT action to cubic order. Subsequently, I will present an algebraic framework, based on Homotopy Algebras, which reproduces gauge invariant DFT to cubic order.
04/03/2022
Generalisations of T- and U-duality have a natural description using doubled and exceptional geometry. In the former case, non-Abelian T-duality (NATD) in particular has proven to be of great use as a technique to generate new (holographic) supergravity solutions in 10 dimensions. This talk will describe some first steps towards finding similar solutions in 11 dimensions based on structures analogous to those present in non-Abelian T-dual solutions, in particular the presence of dual 3-algebra (rather than Lie algebra) structure constants, encoded in a trivector (rather than a bivector). Starting with brane intersecting solutions in type IIA I will generate a new 11-dimensional solution, describe how its AdS limit fits into a class of already NATD-inspired M-theory AdS_3 solutions, and discuss the appearance of an additional E6-valued six-vector deformation.
18/02/2022
The topological A/B-model have been important tools for studying both string theory and the geometry of Calabi-Yau manifolds. They provide both new geometric invariants of the Calabi-Yau, as well as calculating certain terms in the effective theory of string theory. While topological strings on other special holonomy manifolds have been postulated, they are far less understood. In my talk, I will examine the topological string on G2 and Spin(7) manifolds from the target space perspective. I will show that any special holonomy manifold has a double complex which generalises the Dolbeault complex of Calabi-Yau manifolds and provides the natural candidate for the BRST complex of the topological string. Through this, I will be able to conjecture the cohomology of operators and the 1-loop partition functions of the G2 and Spin(7) topological strings.
04/02/2022
I will start by reviewing the physics of KK bubbles and their higher-dimensional generalizations. Secondly, I will move to discussing slightly more general situations where the shrinking modulus is the string coupling. Subsequently I will focus on cases where a Freund-Rubin flux is present, thus leading to the necessity of introducing a source. Finally, I will discuss the case of massive IIA on a 6-sphere as an explicit realization of the aforementioned mechanism and provide an appropriate physical interpretation.
21/01/2022
The talk is based on arxiv:2103.02476, in collaboration with Jakob Palmkvist. Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of attention due to the fundamental role they play for extended geometry. In the present talk, we discuss tensor hierarchy algebras which are super-extensions of over-extended (often hyperbolic) Kac-Moody algebras. They contain novel algebraic structures. Of particular interest is the extension of an over-extended algebra by its fundamental module, an extension that contains and generalises the extension of an affine Kac-Moody algebra by a Virasoro derivation $L_1$. A conjecture about the complete superalgebra is formulated, relating it to the corresponding Borcherds superalgebra. If time allows, some physics applications and questions will be discussed.
23/07/2021
After a short introduction to the λ-model, I will discuss the construction of integrable deformations by employing an asymptotic limit on λ-deformations of non-compact coset CFTs. Specifically, I will focus on a 2D and a 3D example. After the asymptotic limit, the new models interpolate between a CFT with a linear dilaton and a hyperbolic space in two and three dimensions respectively. The existence of a new zoom-in limit in λ-deformed models will also be discussed.
16/07/2021
I will discuss when a supergravity solution, belonging to a consistent truncation on an internal sphere, is guaranteed to have some degree of separation in its Hamilton-Jacobi equation. This talk is based on https://arxiv.org/abs/2102.12493, where it is shown that such separability can be guaranteed if sufficient isometries along the internal sphere are preserved, in addition to an appropriate restriction of the reduction gauge vectors. A classification of such sufficient "separable isometries" may be of practical use in the generation of separable solutions within a given consistent truncation, which are conveniently amenable to scalar probe calculations. On the other hand, our results suggest that a supergravity solution with a separable massless Hamilton-Jacobi equation may be a tell tale sign that it belongs to an underlying consistent truncation, providing a simple diagnostic in the search for new consistent truncations, as occurred in the motivating example of https://arxiv.org/abs/2004.13031.
09/07/2021
In this talk, I review the definition and applications of EL∞-algebras given in arXiv:2106.00108. EL∞-algebras are generalizations of L∞-algebras comprising weak Lie ∞-algebras, and they have a number of applications within extended geometry. In particular, they clarify the higher symmetry structure of generalized tangent bundles and double/exceptional field theory. They also provide the algebraic origin for data needed in the definition of higher gauge theories such as the tensor hierarchy of gauged supergravity. This Lie ∞-algebraic perspective now provides a clear path towards finite gauge transformations and a global picture of these higher gauge theories.
18/06/2021
I will outline how (exceptional) generalised geometry secretly governs the physics of probe branes. Currents on the worldvolume naturally organise in the same multiplets appearing in the tensor hierarchy, and their current algebra takes a universal geometric form. The technical tool for this is an AKSZ-like construction of a Poisson algebra --- the brane phase space --- from the data of a QP manifold; i.e. from the L_infinity-algebra structure of gauge transformations of the (super)gravity background. This talk will be based on https://arxiv.org/abs/2103.08608.
11/06/2021
I will discuss recent progress towards understanding geometric and holographic aspects of electromagnetic duality in four-dimensional supergravity. More concretely, I will focus on the connection between electromagnetic duality and the existence of new classes of S-fold backgrounds of type IIB supergravity of the form AdS4 x S1 x S5 which are conjectured to correspond to new strongly coupled three-dimensional CFT’s on a localised interface of SYM. I will discuss holographic RG flows on the D3-brane that generically connect anisotropic deformations of SYM in the UV to various S-fold CFT’s in the IR with different amounts of supersymmetry and flavour symmetries. Lastly, a geometric interpretation of axionic deformations will be provided in terms of monodromies on the internal S5 when moving around the S1.
04/06/2021
In recent years much progress has been made in the field of non-relativistic physics. In particular, in this talk I will focus on the journey going from non-relativistic particles to strings and finally to membranes. I will discuss how these theories can be obtained in different ways, e.g. via limiting procedures or via embedding in the more general frameworks of Double Field Theory (DFT) and Exceptional Field Theory (ExFT). These provide tools that are especially useful for understanding the symmetries and degrees of freedom of the theories. An example is given by the scalar Poisson equation which, as we will see, cannot be obtained by variation of an action. DFT/ExFT explain naturally how and why this equation cannot be derived from an action principle.
28/05/2021
After a short review of some salient features of E7 and E8 exceptional field theories, I will formulate their E11 generalisation. This exceptional field theory for the Kac-Moody group E11 combines consistently ideas of Peter West, Olaf Hohm, Henning Samtleben and many others. I will explain in particular how one recovers the eleven-dimensional supergravity Lagrangian, together with an infinity of non-linear duality equations for higher rank tensors including the dual graviton. This is a work in collaboration with Axel Kleinschmidt and Ergin Sezgin.
21/05/2021
Upon dimensional reduction to two spacetime dimensions, (super)gravity exhibits an infinite-dimensional duality symmetry based on an affine Lie algebra. I will review the construction of the associated exceptional field theory which, in the maximally supersymmetric case, provides a (formally) E9-covariant reformulation of eleven-dimensional and type IIB supergravity. I will present two equivalent descriptions of its dynamics, which both rely on a pseudo-Lagrangian supplemented by a twisted self-duality equation, and highlight features which do not appear in other exceptional field theories.
14/05/2021
I will review recent breakthroughs in understanding on-shell heterotic moduli from the past decade, many of which required thinking in terms of generalised geometry, doubled field theory and L-infinity algebras. In most of these formulations an extra set of End(TX)-valued are needed for the description to make sense. These unphysical fields are often given the interpretation of field redefinitions. I will take some modest steps towards an understanding of the moduli problem without these spurious degrees of freedom. In particular, I will describe the cohomology which counts the infinitesimal massless modes.
07/05/2021
Noncommutative field theories have been of interest in string theory for over 20 years, originally as effective worldvolume theories of D-branes in B-field backgrounds, and more recently as AdS/CFT interpretations of deformations of integrable string sigma-models. But despite extensive work on the topic, many open questions remain concerning their construction. In this talk I will describe a new class of noncommutative field theories, building on many older works in the literature, which possess 'braided gauge symmetries'. Their construction is motivated by recent attempts to relieve the constraints imposed by conventional star-gauge symmetries and their tension with twisted diffeomorphisms, and by the modern perspective on classical field theories based on homotopy algebras. I will review all of the necessary background, focusing on the case of diffeomorphism invariant theories for illustration. As an example, I will show how these considerations lead to a new theory of noncommutative gravity in four dimensions within the Einstein-Cartan-Palatini formalism.
30/04/2021
A classical E(d(d))-invariant Hamiltonian formulation of world-volume theories of the typical p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d≤6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the E(d(d)) generalised Lie derivative. In this talk I will, starting from a review of the well-known O(d,d)-case of that construction -- the E-model --, discuss the M2-brane in the SL(5)-theory before, motivated by that, introduce the general case. Also the possibilities of deriving the current algebra from a canonical Poisson structure, and the connection of the latter to para-Hermitian exceptional geometry is discussed. This talk is based on https://arxiv.org/abs/2103.03267.
23/04/2021
In this talk I will discuss solution-generating techniques of supergravity and canonical transformations of σ-models using the framework of the flux formulation of Double Field Theory (DFT). Given that the DFT equations of motion as well as the Poisson brackets of two-dimensional sigma models can be written in terms of the so-called generalised fluxes, I will discuss within certain assumptions a classification of transformations which leave these fluxes invariant but transform the background non-trivially. We will assume a generalised Scherk-Schwarz ansatz for the generalised vielbein, such that it takes a twisted form, and that the twist gives rise to constant generalised fluxes on the strong constraint. Furthermore the twist is required to take a particular form when the H-flux is non-vanishing. The classification of maps thus obtained include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of them. This talk is based on https://arxiv.org/abs/2102.04498.
16/04/2021
In the talk I will describe the concept of G-algebroid, which generalises both Lie and Courant algebroids, as well as the Leibniz algebroids used in the description of exceptional generalised geometry (at least for n<7). I will discuss a classification result in the "M-theoretic exact" case and then employ G-algebroids to define and study a general concept of "Poisson-Lie duality", recovering in particular the recently introduced Poisson-Lie U-duality. This is a joint work with Mark Bugden, Ondrej Hulik, and Daniel Waldram.
09/04/2021
We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of polarisation in the construction of the quantum bundle for the string. Following this perspective we adopt a variety of techniques from geometric quantisation to study the doubled space. One application is the construction of the double coherent state that provides the shortest distance in any duality frame and a stringy deformed Fourier transform.
26/03/2021
I will present recent work on the formulation of the classical equations of string and membrane sigma-models in terms of generalised geometry. In particular, I will show that these objects can be thought of as integral surfaces/volumes of generalised vector fields satisfying a natural analogue of the auto-parallel condition.
19/03/2021
We construct a generalization of the three-dimensional Poincaré algebra that includes color group factor and can be used to define a Colored Gravity theory allowing for Minkowski background. We study the corresponding generalization of the free particle model using non-linear realization.
12/03/2021
Although gauge redundancy is a fundamental feature of any gauge theory, any physical observable that we compute must be gauge invariant. One way to combat gauge redundancy is to reformulate the theory in terms of gauge invariant quantities, as is commonly done in cosmological perturbation theory. In this talk, I will discuss how to systematically formulate perturbation theory in gauge invariant variables to all orders in perturbations, via homotopy transfer in the framework of L-infinity algebras. In particular, I will show how this method can be applied to cosmological perturbation theory.
05/03/2021
Dimensional reduction has played a central role in many of the developments in the understanding of string theory and M-theory. Some dimensional reductions are simple and easily understood, such as reduction on a circle or torus. Some are more subtle, such as the reduction of D=11 supergravity on S^7 to give four-dimensional gauged N=8 supergravity. It became clear that the consistency of such reductions was intimately associated with supersymmetry, and more recently, with double field theory. But it was conjectured in 1986, and proven in 2015, that non-trivial group manifold consistent reductions of the effective action for the bosonic string in any dimension also exist, and for these true supersymmetry obviously cannot play a role. The arbitrary-dimensional bosonic string can nevertheless be pseudo-supersymmetrised (i.e. supersymmetry modulo quartic fermion terms), and this can provide a way to understand the consistent reductions. In recent work, we have shown that the N=1 supersymmetric extension of DFT for the bosonic string extends also to a pseudo-supersymmetric DFT, in arbitrary dimension, which draws together the strands of the consistent truncation story.
26/02/2021
The manifestly O(D,D) symmetric formulation known as Double Field Theory (DFT) has proven very useful in many contexts. I will address the problem of constructing higher derivative invariants in this formalism. In agreement with the literature we find that a quadratic Riemann invariant can be constructed, which can account for the first alpha' correction to the bosonic and heterotic string. However, we find that no cubic or quartic Riemann invariants can be constructed. This suggests that the quartic Riemann terms arising at order alpha'^3 in string theory do not have a DFT embedding.
19/02/2021
In this talk, we discuss duality rules for a large class of scalar, p-form and mixed symmetry tensor gauge theories with single or multiple fields. Employing the method of parent actions and including generalised theta terms, two sets of "Buscher rules" are derived as a generic feature of multi-field gauge theories in self-dual dimensions. This points to a universal treatment of dualities facilitated by a formalism based on graded geometry. Emphasis will be given on the gravitational case, where we present an off-shell formulation of single and double dualities in the presence of a gravitational theta term. Our approach clarifies the origin of this term as the linearised limit of the torsional Nieh-Yan invariant. Finally, we discuss some of its physical consequences in the context of axion gravitodynamics.
12/02/2021
Over the last few years, novel approaches to non-relativistic limits of gravity and string theory have led to a renewed interest in non-Riemannian notions of geometry. In the context of gravity, it was recently understood how Newton-Cartan geometry and non-relativistic gravity can be obtained from a covariant large speed of light expansion of general relativity. I will briefly discuss this expansion using frames and highlight how non-zero torsion appears naturally in the geometry. Likewise, in string theory, other variants of Newton-Cartan geometry can be used to describe the non-relativistic Gomis-Ooguri limit. These geometries can be incorporated in the language of double field theory, and I will discuss how the corresponding notion of target space Killing vectors can reproduce known worldsheet symmetries of the Gomis-Ooguri string. Finally, I will mention several outstanding issues and possible applications.
05/02/2021
I will describe the four-derivative corrections to four-dimensional N=2 minimal gauged supergravity and show that they are controlled by two constants. Interestingly, the solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. I will use this to arrive at a general formula for the regularized on-shell action for any asymptotically locally AdS_4 solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way. I will employ these results in the context of holography to derive new explicit results for the subleading corrections in the large N expansion of supersymmetric partition functions on various compact manifolds for a large class of three-dimensional SCFTs arising from M2- and M5-branes. I will also briefly discuss possible extensions and generalizations of these results.
29/01/2021
String theory can be well-defined on spaces without a geometric description. A certain class of such backgrounds is called non-geometric and can be characterized in terms of non-geometric fluxes. Compactifying string theory in the presence of non-geometric fluxes may give rise to stable de-Sitter vacua, however, this is in conflict with the Swampland De-Sitter Conjecture which states that such vacua should not exist in any consistent theory of quantum-gravity. The main purpose of this talk is to address this issue: I will first briefly review non-geometric flux compactifications and revisit known de-Sitter constructions based on non-geometric fluxes. I will then argue for a condition on the tadpole contributions, which excludes known non-geometric de-Sitter vacua.
22/01/2021
In this talk I will show how Generalised geometry provides a general framework to study consistent truncations of M-theory and string theory with different amount of supersymmetry, based on the notion of generalised G-structure. The generalised G-structure contains all the information about the truncated theory: field content. supersymmetry and gaugings. I will discuss in details the cases of half-maximal and one-quarter supersymmetric reduction and illustrate the general construction with few examples.
11/12/2020
In this talk I will describe a model of (double) kinetic theory which paves the way to describe matter in a Double Field Theory background (2003.09588). In this approach, generalized diffeomorphisms acting on double phase space tensors are defined and the generalized covariant derivative is replaced by a generalized Liouville operator. The section condition is consistently extended and the closure of the generalized transformations is still given by the C-bracket. In this context I will introduce a generalized Boltzmann equation and compute the moments of the latter, obtaining an expression for the generalized energy-momentum tensor and its conservation law.
04/12/2020
I will describe the classical interaction between βγ-systems and sigma models displaying the underlying 2d sigma model geometry and the interpretation of the βγ-systems as arising from a quotient with respect to a null Kac-Moody isometry. The presentation will cover purely bosonic, (1,1), (1,2), (2,1) and (2,2) supersymmetric systems.
20/11/2020
Ever since the invention of General Relativity, Riemannian geometry has been privileged to be the mathematical paradigm for modern physics, which enables us to address the very basic notion of `spacetime'. By now, Double Field Theory has evolved to achieve its own autonomy statute as an alternative gravitational theory to GR. Postulating the O(D,D) symmetry as the fundamental principle, GR and the Einstein Field Equations are unambiguously augmented. Further, it turns out that DFT encompasses not only the Riemannian geometry but also non-Riemannian ones where the notion of Riemannian metric ceases to exist. In this talk, after reviewing the above aspects of DFT, I will talk about my latest paper with Shigeki Sugimoto (arXiv:2008.03084), where we examined some quantum consistency of the non-Riemannian geometries as string theory novel backgrounds. The critical dimensions turn out to be the same as in the Riemannian cases (i.e. D=26 or 10). The BRST string spectrum differs, but still agrees with DFT or the Einstein Double Field Equations.
13/11/2020
In the homotopy algebra formulation of field theory, the algebraic operation of "homotopy transfer" is a generalised Wilsonian effective field theory construction. I will outline how homotopy transfer applies to the construction of double field theory beyond cubic order (without the "strong constraint"), and discuss the relation to a proposal by A. Sen.
I will also discuss certain apparently hitherto unknown subtleties of strings on tori which arise along the way, relating to (non)commutativity, sign factors, and the zero-mode sector.
06/11/2020
We revisit the question whether the worldsheet theory of a closed string admits a global O(d,d,R) symmetry. We consider the truncation of the target space theory in which fields are independent of d coordinates, which is O(d,d,R) invariant.
The worldsheet theory is not O(d,d,R) invariant, unless it is truncated by setting winding and center-of-mass momenta to zero. We prove consistency of this truncation and give a manifestly O(d,d,R) invariant action, generalizing a formulation due to Tseytlin by including all external and internal target space fields. It is shown that, due to chiral bosons, this symmetry is anomalous. The anomaly is cancelled by a Green-Schwarz mechanism that utilizes the external B-field.
30/10/2020
I will present a generalization of the conventional Kerr-Schild (KS) formalism, a powerful tool for constructing exact solutions in general relativity, to the double field theory (DFT), exceptional field theory (ExFT) and supergravities. First, a universal structure of the KS ansatz for the generalized metric for DFT and ExFT will be introduced. I’ll show that their equations motion reduce to linear partial differential equations. Based on this formalism, I’ll discuss the exact double copy map, which represents solutions of the supergravity equations in terms of solutions of the Maxwell equation.
23/10/2020
This talk describes an attempt to amend a scheme originally proposed by M. Gell-Mann to identify the spin-1/2 fermions of N=8 supergravity with the quarks and leptons of the Standard Model. This proposal relies in an essential way on embedding the SU(8) R symmetry into the infinite-dimensional `maximal compact' subgroup K(E10) of the conjectured duality symmetry E10. I will also mention more recent work exploring the possible role and significance of the eight massive gravitinos in astrophysics.
16/10/2020
Motivated by their potential to stabilise moduli, we inspect type II backgrounds with gaugino condensates on D-branes. We use the language of generalized complex geometry which is the most adapted to account for their back-reaction. After reviewing the effective 4d physics revealed by Kachru, Kallosh, Linde and Trivedi, as well as the basic concepts of generalized complex geometry, I will show in this talk how the gaugino condensates modify the action and the supersymmetry conditions, concentrating on compactifications to four dimensions, and discuss some of its salient features. We will show how the equations reproduce the phenomenon of moduli stabilisation, and comment on a local solution that matches the on-shell value obtained from the four-dimensional effective action.
09/10/2020
S- and (abelian) T-duality play a central role in string theory, but their scope is limited to highly constrained spacetimes. Generalised T-dualities, which include non-abelian and Poisson-Lie T-duality, apply to a significantly larger class of target spaces with a wide range of applications. Classically they are on an equal footing with abelian T-duality, but their quantum corrections are much more mysterious and mostly unexplored. I will review the main problems which have to be solved to make progress in this direction. Afterwards, I demonstrate how recently explored connections between generalised T-dualities, double field theory, and consistent truncations allow to prove that two-loop RG flows are preserved under these dualities. We will discuss the implications of this result and emphasise how the intriguing mathematical structures that govern all the currentapplications influence quantum corrections in a highly non-trivial way.
02/10/2020
We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to 1/2-BPS branes of the corresponding compactification. We argue that curves of higher genus correspond to non-geometric backgrounds of the M-theory compactifications, which are related to exotic branes. In particular, the number of “special directions” of the exotic brane is equal to the genus of the corresponding curve. In addition to predicting three new non-geometric backgrounds, we discuss a relation between addition of curves in the del Pezzo and the brane polarization effect.
25/09/2020
I will discuss recent work with Ruben Minasian and Yi Zhang on six-dimensional exotic supermultiplets. The main focus of the talk will be on the relationship between these multiplets and exceptional symmetries. In particular I will discuss the non-existence of a standard spacetime "section" for these theories and how the exotic graviton appears in the SL(3,R) Ehlers symmetry term in algebraic decompositions to three dimensions. I will also present an overview of arguments suggesting that the dynamics of these theories may not reduce to those of supergravity in five dimensions and sketch a proposed construction which connects them to three-dimensional supergravity.
18/09/2020
Kaluza-Klein spectra on string/M-theory solutions depend significantly on whether the solution can be obtained from uplift of a maximal gauged supergravity. For some solutions of M-theory, mIIA and IIB obtained from uplift, I will present the spectrum of KK gravitons and discuss a persistent form of universality when solutions with same (super)symmetry and supergravity spectrum are present in different theories. The masses thus found can be obtained from an SL(8)-covariant mass matrix whose trace provides the universal coefficients.
In the second part of the talk, I will discuss the spectrum of KK gravitons around the N=2 AdS_4 solution that is dual to the IR of a cubic deformation of ABJM. This solution cannot be obtained from uplift of an N=8 D=4theory, and this seems to be linked to the fact that its metric cannot be isometrically embedded in R^8. Further, the allocation of modes with different spins in N=2 supermultiplets cannot be made KK level by KK level, but needs space invaders.
11/09/2020
Exotic supergravities are six-dimensional theories with chiral maximal (4,0) and (3,1) supersymmetry, which instead of a graviton feature exotic gauge fields with non-standard Young tableaux representations, subject to selfduality constraints. After reduction to 5D they all share the field content of standard maximal supergravity. While so far these theories are only known in the free limit, their interacting versions were conjectured by C. Hull to exist and to describe strong coupling limits of N=8 theories in 5D.
I present novel actions in a 5+1 split of coordinates whose field equations reproduce those of the free bosonic (4,0) and (3,1) theory, respectively, including the selfduality relations. I discuss evidence for a master exceptional field theory formulation with an extended section constraint that, depending on the solution, produces the (4,0), (3,1) or the conventional (2,2) theory.
04/09/2020
Higher differential geometry is a generalization of differential geometry, where ordinary geometric structures are replaced by their L∞-versions (such as L∞groups and L∞algebras). This formalism let the concept of principal bundle be generalized to the one of "bundle gerbe". This geometric object can be equipped with a connection, whose parallel transport is defined on surfaces instead of on paths. This will be exactly the global formalization of the Kalb-Ramond field. We can then say that bundle gerbes are for strings what principal bundles are for gauge particles.
Double Field Theory is often referred to as a generalization of Kaluza-Klein Theory that unifies a metric and a Kalb-Ramond field, instead of a gauge field. Can this statement be made geometrically precise? In this talk I will give a simple introduction to higher differential geometry, then I will explore the idea that DFT can be naturally globalized in this geometric formalism. Finally I will apply this construction to obtain some examples of T-duality.
28/08/2020
In this talk I will review results obtained by our group over the last few years concerning the calculation of alpha' corrections of 4- and 5-dimensional stringy black-hole geometries and the computation of their Wald entropies, always in the context of the Heterotic Superstring effective action.
First, I will describe the corrections to that action in the Bergshoeff-de Roo formalism and how we can compute the corresponding corrections to the simplest 5- and 4-dimensional (3- and 4-charge) stringy black holes.
Then, I will comment on the problems surrounding the application of the Iyer-Wald prescription to the calculation of the Wald entropy of those black holes directly in terms of their 10-dimensional oxidized counterparts and I will argue that the calculation has to be done using the 4- and 5-dimensional actions.
I will then show how to obtain these actions by direct dimensional reduction and how they provide us with alpha'-corrected T-duality rules. I will derive duality invariant Wald entropy formulas using the Iyer-Wald prescription and I will show that the entropies obtained satisfy the expected properties.
Finally, I will comment on the many unresolved problems related to all these issues.
07/08/2020
The AdS_3/CFT_2 correspondence provides the best arena to test the holographic paradigm. This is simultaneously due to the relative tractability of 2d CFTs and the world sheet theory on AdS_3 backgrounds. Despite this, when compared to their higher dimensional counterparts, little effort has been made to construct AdS_3 string vacua. I will discuss an ongoing program to fill this gap.
There exists a rich variety of superconformal algebras in 2d, with distinct options even for a fixed number of supercharges. This makes the problem of classifying holographic duals to CFTs realising these both interesting and broad. I will discuss how one may systematically realise the various algebras in supergravity, and make use of G-structure techniques to find new classes of solutions in 10 and 11 dimensions. Particular emphasis will be given to a class of solutions in massive IIA preserving small N=(4,0) supersymmetry, for which there is a concrete proposal for dual CFTs.
31/07/2020
Exceptional field theory (ExFT) provides a framework where T and U-duality can be made manifest. In this talk, I will discuss how supersymmetry can also be made manifest in a superspace ExFT. In this approach, the fermionic coordinates are unified with the external spacetime coordinates, which together are acted on by external superdiffeomorphisms. The internal space and its section condition remain purely bosonic. This corresponds to the simplest way one might construct an exceptional superspace, but even this proves surprising: it cannot be done directly with the original supersymmetric formulations of ExFT, and one must instead relax or reformulate certain features (such as the vielbein postulates). I will sketch how this works for the case of E_7. The superspace Bianchi identities then lead to the explicit form of the on-shell p-form curvatures as well as their duality relations. Various applications will also be discussed.
24/07/2020
Generalised geometry has proven to be a central framework to understand T- and U-duality. In particular it provides a critical language to understand two-dimensional deformations of non-linear sigma-models on group manifolds and coset spaces which admit Poisson-Lie symmetry. This latter can be seen as a relaxation of the notion of isometry allowing one to perform a generalised notion of T-duality. In this talk I will discuss joint work with F. Hassler, G. Piccinini, D. Thompson, where we studied integrable deformations of CPn background. Notwithstanding the à priori complexity of these deformations, we show how the deformed CPn background is an example of a bi-Hermitian or generalised Kähler geometry. In addition we explain how the generalised Kähler potential can be constructed for the deformed CPn geometry and provide explicit forms for n=1,2.
17/07/2020
L-infinity algebras are a generalization of Lie algebras involving,besides a 2-bracket, a potentially infinite number of higher-order brackets which satisfy generalized Jacobi identities. In particular, the usual Jacobi identity for the 2-bracket is violated by terms involving a 3-bracket. Originally discovered in physics in the context of closed string field theory, it has since been understood that an L-infinity algebra can in fact be associated to any classical field theory; the Jacobi identities then encode gauge-invariance of the equations of motion, Noether identities and all that, in a way similar to the BRST-BV field-antifield formalism.
In this talk, I will first review the definition of L-infinity algebras, in two complementary ways: 1) the original formulation involving an infinite number of brackets, which can be neatly packaged in a nilpotent coderivation, and 2) the dual picture, where L-infinity relations are encoded in a nilpotent derivation. (For field theories, this derivation is nothing but the BRST-BV differential.) Then, I will explain the mathematical notion of homotopy transfer: how, under certain conditions, the L-infinity structure can descend to a subspace of the original vector space. In the field theory context, this corresponds to the notion of (tree-level) integrating out of degrees of freedom, with the smaller L-infinity algebra encoding the algebraic structure of the effective theory.
This is based on work in progress with Alex S. Arvanitakis, Chris Hull and Olaf Hohm.
10/07/2020
Supergravity theories can be consistently truncated to lower dimensional gauged supergravities, which has many applications especially for the purpose of solution generation. A much studied class of truncations are generalised Scherk–Schwarz (gSS) reductions. While the principle of such truncations is well-understood and many examples are known, there is no complete classification of gSS reductions. Conversely, it can be difficult to know if a specific gauged supergravity can arise from a generalised Scherk–Schwarz truncation of some higher-dimensional model.
I will review some results on the general recipe for constructing generalised Scherk–Schwarz uplifts of gauged supergravities and on the conditions for such uplifts to exist. I will then discuss work in progress in rephrasing such uplift conditions as linear constraints and comment on the extension to three-dimensional gauged supergravities and lower, where the associated exceptional geometries become more complicated.
26/06/2020
We show that Non-Abelian T-duality (NATD) can be described as a coordinate dependent O(D,D) transformation for supergravity fields in the NS-NS sector and as a Pin(D,D) transformation for the fields in the RR sector. This enables us to show that NATD is a solution generating transformation in Double Field Theory (DFT), by regarding the transformed fields as duality twisted fields in the context of Gauged Double Field Theory (GDFT) of Type II strings. When the isometry algebra is non-unimodular, consistency of GDFT forces the generalized dilaton field to have a linear dependence on the winding type coordinates of DFT, implying that the transformed fields satisfy the field equations of DFT in the generalized supergravity frame. We also discuss briefly the analogous story for Yang-Baxter deformations.
19/06/2020
Gauged supergravity as well as double and exceptional field theory can be formulated in terms of a hierarchy of duality relations between curvatures originating from the tensor hierarchy. The needed higher algebraic structures can be derived from a differential graded Lie algebra. I outline how exceptional field theory fits into this scheme by showing that its generalized geometric structures can be naturally interpreted in terms of an embedding tensor map and an infinite-dimensional Lie algebra.
12/06/2020
T-duality implies that string theories, once compactified on a d-dimensional torus, must have a global O(d,d) symmetry. The exact interplay between this duality and α'-corrections is however not known. In this talk, I will expose new tools to tackle this problem and show, considering the bosonic string theory to first order in α', that this symmetry requires a Green-Schwarz type mechanism for α'-deformed O(d,d) transformations.
05/06/2020
Consistent truncations of ten- and eleven- dimensions supergravity are useful tools in order to derive lower-dimensional effective theory, but are usually difficult to obtain. Generalised geometry provides a well suited framework to derive consistent truncations in arbitrary dimension and with different amount of supersymmetry, based on the notion of generalised G-structure. In this talk I will present first the general ideas in generic dimension and amount of supersymmetry. Then I will show how to apply the formalism to truncations to half-maximal supergravity in five dimensions. As concrete examples, I will present an M-theory truncation that contains the Maldacena Nunez solutions for M5-branes wrapped on a Riemann surface.
29/05/2020
Starting with some particular physical theory, we are often interested in then exploring the space of all physical theories either by adding deformations or taking limits. I will describe a connection between two seemingly unrelated such explorations. The first is the TTbar deformation of two-dimensional field theories. The second is the non-relativistic limit of string theory. It is well-known that the TTbar deformation of D free bosons leads to the Nambu-Goto action in D+2 dimensions; I will explain how the limit where the deformation parameter returns to zero can be viewed as a non-relativistic limit of the string. In order to describe and generalise this correspondence, I will use intuition gained from the O(D,D) covariant "doubled" formulation of string theory geometry. This is natural here as TTbar deformations can be viewed as TsT or bivector transformations, while non-relativistic limits which are singular in terms of the standard spacetime geometry become well-defined in terms of doubled variables. Time permitting I will say something about possible generalisations using exceptional geometry.
22/05/2020
Local (i.e. non-constant) beta shifts of O(D,D) are a solution-generating technique in supergravity, when additional conditions are imposed on beta. In the literature this construction has been known as "homogeneous Yang-Baxter deformation", and it was first introduced to generate integrable deformations of 2d sigma-models. Interest on such deformations is also motivated by their relation to non-abelian T-duality. In this talk I will review some aspects of this subject and I will explain how to obtain alpha'-corrections for the deformed backgrounds by exploiting the Double Field Theory formulation.
16/05/2020
Understanding the geometry of flux backgrounds of string theory and M-theory is an important problem in phenomenology. Most attempts at this require studying backgrounds according to torsion classes, or treating the flux perturbatively through moduli stabilisation. However, in both cases we either lose analytic tractability by losing the integrable G-structures that characterise the fluxless backgrounds, or we get only approximate results for small flux. In this talk we will show that generic flux backgrounds can be described by integrable SU(7) structures in exceptional generalised geometry. These structures have properties reminiscent of conventional complex structures, being described by an involutive subbundle of the generalised tangent bundle, and a vanishing moment map. Using this structure we will be able to find the exact moduli of broad classes of flux backgrounds. This description of flux backgrounds also provides a new interpretation of G2 manifolds, which may have interesting links with geometric invariant theory and new exceptional Hitchin functionals.
08/05/2020
I will discuss how exceptional field theory can be used to compute aspects of the low-energy effective field theory description of type II string theory. Since exceptional field theory also includes the description of (exotic) branes, one can also determine the exact non-perturbative contributions to certain higher-derivative couplings. Emphasis will be put on recent advances for 1/8-BPS couplings that are connected to tropical limits of string invariants at genus two.
01/08/2020
In this talk, I will show how exceptional field theory gives us a powerful new method for computing the Kaluza-Klein spectrum of string theory compactifications. In particular, we can easily compute the Kaluza-Klein spectrum for any vacuum of an N=8 gauged supergravity arising from a consistent truncation. This includes various AdS vacua in 4 and 5 dimensions, preserving few or no (super)symmetries. I will apply this new method to compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3) x SO(3) invariant AdS_4 vacuum of 11-dimensional supergravity, which is perturbatively stable within N=8 gauged supergravity. I will show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS_4 vacuum is unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes.
24/04/2020
Non-Abelian and Poisson-Lie generalised notions of T-duality have proven to be useful tools in holography, both as solution generating techniques and as paradigms for integrable deformations. Motivated by this, we examine if a similar idea of “non-Abelian U-duality" can be defined and found within M-theory. Here I will report on recent progress detailing how the generalised geometry foundation of Exceptional Field Theory provides a tractable starting point to determine the algebraic structure that would be required to support this.
17/04/2020