Integrability, Dualities and Deformations
Archive of talks of the online seminar series Integrability, Dualities and Deformations
Here you can find the slides and recordings of past talks. Note that the discussion session following each talk is not recorded.
24 March 2021
Matthias Staudacher (Humboldt University Berlin) – The Integrable Hypereclectic Spin Chain
Abstract: I discuss the features of certain integrable spin chains one obtains from the dilatation operator of strongly twisted, double-scaled deformations of N = 4 Super Yang-Mills Theory. A particular case is a certain chiral three-state model with an exceedingly simple Hamiltonian. It is non-diagonalizable, and shows very rich and intricate patterns of Jordan cell formation. I explain some of the difficulties one faces when applying the quantum inverse scattering method to these models. Time permitting, I will discuss some relations to logarithmic four-dimensional quantum field theories and in particular the resulting challenges for a complete understanding of fishnet-type models.
Edvard Musaev (Moscow Institute of Physics and Technology) – Deformations of backgrounds of 11-dimensional supergravity
Abstract: Green-Schwarz superstring is known to be integrable on certain backgrounds, e.g. AdS5 × S5. This integrability is preserved upon a certain class of deformations of the target space-time, defined in terms of an r-matrix satisfying classical Yang-Baxter equation. In this talk a generalisation of such deformations to the case of solutions to 11-dimensional supergravity equations of motion. After a very short review of the exceptional field theory formalism we will see that it allows 1) to naturally introduce polyvector deformations of 11-dimensional backgrounds, 2) prove that these are solution generating transformations given an algebraic condition is satisfied. This condition can be understood as a generalisation of classical Yang-Baxter equation and is probably some classical limit of Zamolodchikov tetrahedron equation, which describes three-dimensional integrable systems. Some speculations in this direction and towards the 11-dimensional generalised supergravity will be provided.
10 March 2021
Carmen Núñez (University of Buenos Aires & CONICET) – Supersymmetry, T-duality and heterotic alpha'-corrections
Abstract: In this talk I will discuss the role of supersymmetry and T-duality in constraining the heterotic string alpha'-expansion. I will present the first order higher derivative corrections to N=1 supersymmetric Double Field Theory, which provides a duality covariant description of the heterotic string effective field theory to O(alpha'). I will derive the first order deformations of the transformation rules of the supergravity and super Yang-Mills fields and compare with previous results obtained from supersymmetrization of the gauge and Lorentz Chern-Simons forms.
Marius de Leeuw (Trinity College Dublin) – Integrable deformations of holographic integrable models
Abstract: In this talk I will discuss a new approach to finding solutions of the Yang-Baxter equations. By using this approach I will classify 4x4 solutions of the YBE and show that they contain the AdS2 and AdS3 S-matrices. In this way I will classify integrable deformations of these holographic integrable models and I will discuss some of their properties.
24 February 2021
David Skinner (University of Cambridge) – Twistors, Integrability and 4d Chern-Simons Theory
Abstract: It has long been known that many classical integrable systems can be obtained as symmetry reductions of the anti-self-dual Yang-Mills equations. Following a suggestion of Costello, I’ll show that actions for asd YM arise from holomorphic Chern-Simons theory on twistor space, defined with the help of a choice of meromorphic (3,0)-form. Applying the symmetry reduction in twistor space, one instead arrives at the description of the integrable system in terms of 4d Chern-Simons theory of Costello & Yamazaki.
Sibylle Driezen (IGFAE, Santiago de Compostela) – Supergravity solution-generating techniques and canonical transformations of σ-models from O(D,D)
Abstract: 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 in particular 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. The assumptions include 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 arXiv:2102.04498.
10 February 2021
Nat Levine (Imperial College London) – RG flow of integrable GxG and GxG/H sigma models
Abstract: I will present new results on the RG flow of integrable sigma models on product spaces G×G and G×G/H with Wess-Zumino terms. These integrable theories were originally derived from affine-Gaudin models. We study their RG flows at 2-loop order and find that they are stable under the RG flow, agreeing with expectations from integrability. An interesting special case of the SU(2)×SU(2)/U(1) model is an integrable model on T^{1,1} with a particular B-field. We point out that this model actually generalizes to an integrable model on T^{1,Q} by putting unequal WZ levels on the two SU(2) factors. Based on a paper in preparation with Arkady Tseytlin.
Daniel Thompson (Swansea University) – Resurgence in the Bi-Yang-Baxter Model
Abstract: Two-dimensional integrable QFTs provide a tractable arena in which to test the idea of "resurgence": a conjectured set of intricate relations between large order asymptotic behaviour of perturbative expansions and non-perturbative sectors. This talk explores aspects of resurgence in the context of two-parameter integrable (bi-Yang-Baxter) deformations of the Principal Chiral Model. We identify finite action Euclidean field configurations called Unitons. A twisted spatial reduction of this theory results in a quantum mechanics with an elliptic potential. We show how the Unitons give a non-perturbative contribution precisely in agreement with the large order behaviour of this quantum mechanics. We also point out some intriguing connection between the WKB analysis of this QM and N=2 Seiberg Witten theory.
27 January 2021
Pavol Ševera (University of Geneva) – Dualities, boundary conditions, and RG flow
Abstract: I will explain how to obtain Poisson-Lie T-duality from Chern-Simons theory sandwiched between two boundary conditions (a picture which generalizes to other dimensions) and how to compute the 1-loop beta function out of this picture. Based on arXiv:1602.05126, arXiv:1909.06151 with Ján Pulmann and Fridrich Valach, and arXiv:2009.00509 with Ján Pulmann and Donald Youmans.
Carlos Núñez (Swansea University) – Aspects of Gauge-Strings Duality. Integrability and Holography
Abstract: I will discuss the holographic description of CFTs in diverse dimensions. I will comment on the possibility of finding some CFTs that are integrable. This presentation is based on papers that I wrote in the last one and a half years, with various colleagues.
13 January 2021
Dmitri Bykov (Steklov Mathematical Institute, Moscow) – Sigma models as Gross-Neveu models
Abstract: I will show that there is a wide class of integrable sigma models, which includes CP^{n-1}, Grassmannian, flag manifold models, that are equivalent to bosonic (and mixed bosonic/fermionic) chiral Gross-Neveu models. The established equivalence allows to effortlessly construct trigonometric/elliptic deformations, provides a new look on the supersymmetric theory and on the cancellation of anomalies in the integrability charges. Using this formalism, we develop criteria for constructing quantum integrable models related to quiver varieties. Based on arXiv:2006.14124 and arXiv:2009.04608.
Falk Hassler (Texas A&M University) – One- and two-loop RG flows of integrable E-models
Abstract: There is an intriguing connection between integrable sigma-models and Poisson-Lie (PL) symmetry. As I will review, the latter is manifest in the E-model, rendering it a powerful tool to construct a variety of integrable models which recently have been identified with surface defects in 4d Chern-Simons theory. Manifest PL symmetry facilitates computations which would be forbiddingly complex without it. Important examples, which I will discuss in detail, are one and two-loop beta-functions. We will see that they underpin a deep connection between classical integrability and the corresponding quantum regime. Based on arXiv:2012.10451 and arXiv:2011.15130 with Thomas Rochais.
16 December 2020
Bogdan Stefański, jr. (City University London) – Chern-Simons Origin of Superstring Integrability
Abstract: I will review how four-dimensional Chern-Simons gauge theory provides a unified framework for a variety of integrable models. I will then show how the AdS5 × S5 Green-Schwarz superstring can be obtained from a modification of 4d CS theory: the Beltrami-Chern-Simons theory. This reformulation of the superstring provides a new way of understanding integrable holography in terms of a (relatively) simple gauge theory as well as the relations between different worldsheet formulations of superstrings.
Slides – Recording
Roberto Tateo (University of Torino) – Irrelevant deformations of soliton theories
Abstract: Two-dimensional field theories deformed by Zamolodchikov's TTbar operator have recently attracted the attention of theoretical physicists due to the many important links with integrability and string theory. In this talk, I will describe various classical and quantum aspects of this irrelevant perturbation, in particular the deformation of classical soliton models.
2 December 2020
Michela Petrini (Sorbonne University) – Exactly marginal deformations of superconformal gauge theories
Abstract: We study the supergravity dual of the conformal manifold of the N = 1 superconformal field theories. Using generalised geometry, we show that the data of the background geometry is encoded by certain holomorphic objects, dual to the superpotential of the field theory. This provides a solution to the longstanding problem of finding the gravitation dual of the generic N = 1 deformations of N = 4 conformal field theory. Using this formalism, we derive a new result for the Hilbert series of the deformed field theories.
Linus Wulff (Masaryk University) – Alpha'-correction to generalized dualities and deformations from O(D,D)
Abstract: Generalizations of T-duality such as non-abelian and Poisson-Lie T-duality are powerful solution generating techniques in supergravity. They have also been used to construct integrable deformations of string sigma models. Until recently these constructions were only understood at the supergravity level. As a first step towards an understanding at the quantum level I will describe how the O(D,D)-covariant formulation of supergravity à la Double Field Theory can be used to find the first alpha'-correction, rendering the string sigma model Weyl-invariant up to two loops.
18 November 2020
Ctirad Klimčík (Aix-Marseille University) – T-duality and T-folds for point particles
Abstract: I argue that the T-duality phenomenon is not exclusively a stringy effect but it is relevant also in the context of the standard point particle dynamics. To illustrate the point, I describe the construction of a four-parametric family of four-dimensional electrogravitational backgrounds such that the dynamics of a charged point particle in those backgrounds is insensitive to a particular permutation of the parameters although this very permutation does alter the background geometry. In particular, I show that a direct product of the Euclidean plane with the two-dimensional Euclidean black hole admits a point-particle T-dual with asymptotically negative curvature. For neutral particles, this point-particle T-duality picture gets slightly modified because the T-duality map is no longer defined everywhere but only on a dense open domain of the space of states. The exceptional states sitting outside of the domain of definition can be then naturally interpreted in terms of a point particle T-fold.
Alessandro Torrielli (University of Surrey) – How one massless TBA was exactly solved
Abstract: We review the exact solution of the massless relativistic Thermodynamic Bethe Ansatz which describes the non-trivial BMN limit of massless right-right and left-left scattering in AdS3 × S3 × T4 superstring theory. The exact solution is achieved thanks to the absence of bound states, which produces a compact system of few equations amenable to Zamolodchikov's dilogarithm trick. This massless TBA describes a CFT, whose central charge is computed exactly. This is work done in collaboration with Diego Bombardelli and Bogdan Stefanski in arXiv:1807.07775.
4 November 2020
Larisa Jonke (Ruđer Bošković Institute) – DFT algebroid and Lie_infinity algebra
Abstract: Double field theory (DFT) is a proposal to incorporate the T-duality symmetry of string theory as a symmetry of a field theory defined on the double configuration space. However, the theory is constrained in the sense that, although all coordinates are doubled, the physical fields and parameters depend only on half of them. This strong constraint makes DFT a well-defined theory, and in particular it enforces closure of the symmetry algebra of the theory. On the solution of the strong constraint the relevant bracket of the symmetry algebra of DFT reduces to the Courant bracket.
In this talk I will present a proposal for a geometric structure based on the C-bracket of DFT, called DFT algebroid, and discuss its properties in the framework of L_infinity algebra. The analysis provides a useful step towards coordinate invariant descriptions of DFT and construction of the corresponding sigma-model.
Fiona Seibold (ETH Zurich) – Advances in integrable eta-deformed superstrings
Abstract: eta-deformations of the AdS5 × S5 superstring are integrable models with quantum-deformed symmetry. Several puzzles associated to these models have recently been resolved. In this talk I will present the salient features of eta-deformations and discuss these recent advances. I will explain in which cases the deformed backgrounds solve the supergravity equations of motion and discuss the worldsheet scattering matrices for these theories, showing compatibility with integrability and quantum-deformed symmetry. Based on arXiv:1811.07841 with B. Hoare and arXiv:2007.09136 with S. van Tongeren and Y. Zimmermann.
21 October 2020
Konstantinos Sfetsos (University of Athens) – The free field approach to λ-deformed CFTs
Abstract: The structure of the λ-deformed σ-models can be explored by setting up a perturbative expansion around the free field point. Unlike previous approaches, the advantage of this one is that all deformation effects are explicitly encoded in the couplings of the interaction vertices and in the λ-dressed operators. We show how to compute anomalous dimensions of operators, elementary and composite, as well as the β-function of the deformation parameter. We consider λ-deformed current algebra as well as coset CFT's. We point out feature directions in which this approach could be particularly useful.
Balázs Pozsgay (Eötvös Loránd University, Budapest) – Current operators in integrable spin chains: brief review
Abstract: In this talk we review the recent progress on current operators in integrable models. These operators are relevant for at least three purposes:
1. They describe the flow of conserved charges and they are central to the theory of Generalized Hydrodynamics, describing transport phenomena.
2. They are perturbing operators for the so-called long range deformations, which are relevant to AdS/CFT. This includes the TTbar-type (also called bilocal) deformations.
3. They are connected to the theory of factorized correlation functions, and their mean values in the eigenstates have a remarkably simple form.
We will review these three topics, and we will also present a new algebraic construction for the current operators, which uses the very basic tools of Algebraic Bethe Ansatz.
7 October 2020
Benoît Vicedo (University of York) – From 4d Chern-Simons theory to 2d integrable field theories via edge modes
Abstract: Four-dimensional Chern-Simons (4d CS) theory in the presence of surface defects was proposed by Costello and Yamazaki as a unifying framework for describing two-dimensional integrable field theories (2d IFTs). I will describe a new way of understanding the passage from 4d CS to 2d IFTs. Specifically, I will show that (a suitably regularised version of) the 4d CS action becomes gauge invariant if certain boundary conditions are imposed on the surface defects. Alternatively, the action can be made gauge invariant by coupling it to a new 2d field, the edge mode, localised on the surface defects. I will then explain how the edge mode perspective on 4d CS provides a direct link to 2d IFTs. The talk will be based on the joint work arXiv:2008.01829 with M. Benini and A. Schenkel.
Chris Blair (Vrije Universiteit Brussel) – Exploring Exceptional Drinfeld Geometries
Abstract: I will describe geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. I will first introduce the essential algebraic ideas and then discuss some geometric examples. Based on arXiv:2006.12452 with D. Thompson and S. Zhidkova.