Poster Session

The content of the poster is mainly based on the results proposed in [2402.08719] on the study of topological defects in two dimensional Non-linear sigma models on K3, which provide the simplest examples of Calabi-Yau compactifications in type II string theory. In the paper we consider topological defect lines commuting with the spectral flow and the whole N = (4, 4) superconformal symmetry. By studying their fusion with boundary states, we derive a number of general results for the category of such defects. We argue that while for certain K3 models infinitely many simple defects, and even a continuum, can occur, at generic points in the moduli space the category is actually trivial, i.e. it is generated by the identity defect. Furthermore, we show that if a K3 model is at the attractor point for some BPS configuration of D-branes, then all topological defects have integral quantum dimension. We also conjecture that a continuum of topological defects arises if and only if the K3 model is a (possibly generalized) orbifold of a torus model. Finally, we test our general results in a couple of examples, where we provide a partial classification of the topological defects.

We study infinite-distance limits in the moduli space of perturbative string vacua. The remarkable interplay of string dualities seems to determine a highly non-trivial dichotomy, summarized by the emergent string conjecture, by which in some duality frame either internal dimensions decompactify or a unique critical string becomes tensionless. Assuming the existence of light states, we investigate whether this pattern persists in potentially non-geometric settings, showing that (a proxy for) the cutoff of the gravitational effective field theory in perturbative type II vacua scales with the spectral gap of the internal conformal field theory in the same manner as in decompactification or emergent string limits, regardless of supersymmetry or whether the internal sector is geometric. As a byproduct, we elucidate the role of the species scale in (de)compactifications and show compatibility between effective field theory and worldsheet approaches in the presence of curvature deformations in geometric settings.

Based on 2405.03683

We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d N=2 SCFTs with 1/2-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial S^3. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d N=2 SCFTs on the boundary. In particular we derive the action of the SL(2,Z) duality on the one-point functions.

The study of the spectral problem of planar N=2 SCFTs and their corresponding spin chains has been an inauspicious problem. In this talk I want to present a novel approach to the coordinate Bethe Ansatz which allowed the computation of the three-magnon wave function (paper to appear) for the spin chains that capture the spectral problem of the marginally deformed Z_2 orbifold of N=4 SYM in planar limit. The novel idea is the introduction of contact terms which incorporate the dynamical structure of the spin chains and it can be generalized to n-body problem and also to more general orbifolds.

Six-dimensional superconformal field theories (SCFTs) have an atomic classification in terms of elementary building blocks, conformal systems that generalize matter and can be fused together to form all known 6d SCFTs in terms of generalized 6d quivers. It is therefore natural to ask whether 5d SCFTs can be organized in a similar manner, as the outcome of fusions of certain elementary building blocks, which we call 5d conformal matter theories. We explore this idea by giving a systematic construction of these irreducible "bifundamental" ADE SCFT building blocks, via geometric engineering techniques in M-theory. We then show how these can be gauged together giving rise to 5d SCFTs captured by 5d generalized linear quivers with ADE gauge groups as nodes, and links given by 5d conformal matter. As a bonus, this allows us to exhibit novel 5d dualities. Finally, to further characterize the 5d conformal matter SCFTs, we investigate their dimensional reduction to 4d, as well as their magnetic quivers.

Poster joint with Andrea Sangiovanni

We use branes to generalize the Distance Conjecture. We conjecture that, in any asymptotic distance Delta in the moduli space of string vacua of a D-dimensional theory, among the set of particle towers or branes with at most P<D-1 spacetime dimensions, at least one particle tower or brane becomes exponentially low tension by T~exp(-alpha Delta), where alpha is at least 1/sqrt(D-P-1). Since P can vary, this implies multiple conditions, and the Sharpened Distance Conjecture is the P=1 case. Under assumptions, this conjecture is a necessary condition imposed on higher-dimensional theories in order for the Sharpened Distance Conjecture to hold in lower-dimensional theories. We test our conjecture in multiple 32 and 16 supercharge examples in diverse dimensions and see that it is satisfied and often saturated. Based on work with Ben Heidenreich and Tom Rudelius.

We study limits of vanishing Yukawa couplings in Quantum Gravity, using as a laboratory type IIA orientifolds. We show that in the limit Y → 0 there are some towers (dubbed gonions) that become asymptotically massless, while at the same time, the kinetic term of some chiral fields becomes singular. For limits parametrised by a large complex structure saxion u, Yukawa couplings have a behavior of the form Y ∼ 1/u^r. Moreover, some of the gauge couplings associated with the Yukawa vanish in this limit. The lightest gonion scales are of order mgon ∼ g^s   with s > 1, verifying the magnetic WGC with room to spare and with no need of its tower/sublattice versions.  All these results may be very relevant for phenomenology, given that some of the Yukawa couplings in the Standard Model are very small.

Based on arXiv:2403.09775

The lack of experimental evidence for supersymmetry has recently fueled a resurgence of interest in non-supersymmetric heterotic strings. A detailed analysis was carried out on the possible gauge symmetries and the behavior of the one-loop potential for their circle compactifications. However, no minima were found. Orbifold compactifications lead to theories with reduced-rank symmetries and fewer moduli, making them potentially easier to stabilize. Interestingly, part of the structure underlying the supersymmetric string landscape is retained in these non-supersymmetric variants, allowing us to study these rank-reduced theories in great detail. Furthermore, an analysis of infinite distance limits reveals a complex web that interrelates both known and previously unknown theories.

The generalised Einstein condition is the analogue of Ricci flatness in the context of generalised geometry. From the point of view of physics, this condition naturally arises as one of the equations of motion of the common NS-NS sector of type II and heterotic supergravity theories. We study generalised Einstein metrics on four dimensional Lie groups, achieving a complete classification in the Riemannian case and a partial classification in the Lorentzian case. Based on current work in progress with Vicente Cortés and Marco Freibert.

The goal of the work is to create an axiomatic equivalent to the axiomatics of Haag-Araki and Whiteman, based on the principle of causality for sticky sets.

The new mathematical apparatus proposed in this paper, which includes elements of various interpretations of quantum field theory, nonlinear dynamics and p-addic physics, allows us to solve the problem of constructing a consistent theory for describing compactly generated Cauchy horizons, the vector dominance of the Arnowitt-DeWitt-Mizner energy and others ultrarelativistic effects.

Results:

1. The concept of extended locality of globally hyperbolic sets has been introduced (by introducing a hidden parameter c).

2. A criterion for constructing a network R(O) from a family of sticky sets on a Moran structure is defined.

3. It is proved that such a network is an adhesive network.

4. It is proved that perfectly simple sets with the isotonic property are symplectic.

5. Singular solutions are found in RTG for a geodesic line located outside the light cone

6. It is proved that the polynomial time in the Penner-Kontsevich model is globally hyperbolic

7. The ergodic properties of the temporal ordering operator are studied in the framework of the method of intervals of Markov mappings.

8. The induced integration procedure has been improved using the methods of algebraic field theory

9. The traceless momentum tensor of matter energy 〖T^*〗_(ωλ )

10. The notion of non-continuability is generalized to pseudoholomorphic curves.

11. A spectral approach has been introduced to consider operators of the form T_p

12. A connection has been found between superselection rules and the choice of superlight-speed alternatives

13. A new method for localizing eventually periodic points based on epsilon cycles has been created.

We propose that the M2-brane with fluxes and monodromy can reproduce the type IIB gauged supergravities in nine dimensions. The world-volume description of these M2-branes with nonvanishing winding on a torus is known. They have good quantum properties, such as the discreteness of the supersymmetric spectrum. Their global description is also known and is given in terms of twisted torus bundles with monodromy. We found a relation between the equivalence classes of twisted torus bundles, the local symmetry on type IIB gauged supergravities in nine dimensions, and the discrete values of the mass parameters in the quantum theory. We also find that transformations between inequivalent twisted torus bundles correspond to the U-duality symmetry group, a subgroup of SL(2, Z).

Based on [2312.12510] with M. Sperling. An intriguing class of 6d supersymmetric theories that also exhibit T-duality are known as little strings theories. Particularly noteworthy, are those realised on a single curve of zero self-intersection, for which it is usually possible to engineer brane systems and derive magnetic quivers. A robust feature of these theories is their Higgs branches, which we can study using multiple techniques (including branching rules, brane dynamics, F-theory geometry, quiver subtraction, and the decay and fission algorithm). Therefore, we detail the Higgs branch Hasse diagram and determine the transverse slices for every elementary Higgs branch RG-flow. 

We present some recent and ongoing work about the study of the moduli space curvature along infinite distance limits. We consider the vector multiplet sector of type IIA string theory compactified on a Calabi-Yau three-fold, where such limits can be roughly classified as M-theory limits, F-theory limits or emergent string limits. We discuss the relation between divergences of the scalar curvature, that arise both at the classical level and including quantum corrections, and properties of gauge theory sectors that decouple from gravity. In particular, we focus our attention on the imprint of LSTs and SCFTs on the moduli space curvature.

We present a new technique to derive the quiver and the superpotential of a D2-brane probe at the singularity of a specific class of CY threefolds. These spaces are constructed as non trivial fibrations of deformed ADE singularities on a complex plane and can be conceived as non toric generalizations of the conifold geometry. We establish a correspondence between monopole operator deformations of the 3d superpotential and resolution patterns of the probed geometry.

The landscape of F-theory flux compactifications is expected to be remarkably constrained due to deep insights in Hodge theory and tame geometry. First, we will present new results on asymptotic Hodge inner products, which provide another perspective on the established finiteness of self-dual flux vacua. Subsequently, we motivate three new mathematical conjectures on the enumeration, dimensionality, and geometric complexity of the flux landscape, including a reformulation of the tadpole conjecture.

Black holes are the prime theoretical laboratory to understand the quantum nature of gravity. Thanks to holography, we can use the tools provided by QFT to gain insights on microstates of black holes and their phase transition, but most of the results are for the “basic” example of N=4 SYM. Recently, a step further has been taken by considering the insertion of surface operators in SYM as order parameters for such transition. In this context,  we evaluate the superconformal index of N=4 SYM in the presence of a Gukov-Witten surface defect and compute its backreaction in the Cardy-like limit. In the holographic setup, the defect is implemented by a D3-brane which probes the Black Hole. 

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. In paper 2403.05650, we have already found many examples on T^5 with 0, 1, 2 hypermultiplets. This work focuses on 4-dimension, with more complicated prepotential corrections, including instanton corrections. We prove the corrections to be inconsistent due to dual pair theories and T-duality symmetry.

Most efforts in F theory model building have focused on GUT models based on SU(5) gauge group. Alternatively, other GUT models based on left-right symmetries, such as the Pati-Salam model, are also attractive from a phenomenological perspective, because of the natural realization of neutrino mass mechanism, leptogenesis, and cosmic strings. Since it is hard to fix the spectrum completely from a top-down construction, we start from a bottom-up approach and construct a Pati-Salam model that reproduces all successful phenomenology, especially the flavor hierarchy. The final goal is to connect this bottom-up picture with a top-down approach and match them at the GUT scale, to construct a F-theory inspired Pati-Salam model that can be tested in near-future experiments. 

We analyse the scalar curvature of the vector multiplet moduli space of type IIA string theory compactified on a Calabi–Yau manifold. While the volume of this moduli space is known to be finite, cases have been found where the scalar curvature diverges positively along trajectories of infinite distance. We classify the asymptotic behaviour of the scalar curvature for all large volume limits within the moduli space, for any choice of Calabi-Yau, and provide the source of the divergence both in geometric and physical terms. Geometrically, there are effective divisors whose volumes do not vary along the limit. Physically, the EFT subsector associated to such divisors is decoupled from gravity along the limit, and defines a rigid N = 2 field theory with a non-vanishing moduli space curvature. We propose that the relation between scalar curvature divergences and field theories decoupled from gravity is a common trait of moduli spaces compatible with quantum gravity.  

We study the phenomenological applications of including geometric and non-geometric fluxes to the flux-induced scalar potential for type IIA orientifold compactifications. The resulting potential presents a bilinear structure which we use to explore two topics: scale separation and the search of dS vacua.

First, we generalize the construction of scale-separated vacua in massless Type IIA compactified on an SU(3)-structure manifold with geometric fluxes beyond the double T-dualization of a DGKT toroidal orbifold. We propose new infinite families of vacua based on elliptic fibrations with metric fluxes. They display parametric scale separation, achieved by an asymmetric flux rescaling. 

Second, we perform an analytical exploration of de Sitter conditions in type IIA compactifications with (non-)geometric fluxes along with the standard NS-NS and RR p-form fluxes.  We find four conditions that the scalar fields and fluxes must satisfy to achieve dS vacua, extending previous results in the literature. We then impose an Ansatz in which the F-terms are proportional to the respective Kähler derivatives. In this set-up we can derive additional constraints and to classify the possible dS no-go scenarios in terms of eight axionic fluxes.

Among various predictions of string compactifications, axions hold a pivotal role, as they provide a unique avenue to tie UV physics to experiments. 

Most experimental setups aim to detect a signal using the direct coupling between the axion and the Standard Model. However, string axions do not necessarily need to couple to the Standard Model directly. In this poster I will describe how inflationary models with multiple “spectator" axions coupled with dark gauge sectors via Chern-Simons coupling could source observable gravitational waves. 

If string axions coupled to Abelian gauge fields undergo slow-roll during inflation, they produce a multi-peak GW signal whose magnitude depends on the details of the compactification. I will explain how to embed spectator axions into type IIB orientifold compactifications and the restrictions imposed on such models from consistency and control requirements, thereby motivating models that may live in the landscape as opposed to the swampland.

We investigate the high-energy fixed-angle scattering of pions and rho mesons in a holographic QCD model, following the Polchinski-- Strassler proposal. In agreement with earlier findings of Polchinski, Strassler and other authors, we observe partonic behaviour coming from string amplitudes in AdS spacetime. In our holographic approach, 2-to-n pion scattering amplitudes display agreement with known constituent counting rules found in QCD and other asymptotically free confining gauge theories. However, in naïve disagreement with these rules, we further report that 2-to-n scattering amplitudes that involve rho mesons, and where all the other scattered states can be pions, are suppressed in Mandelstam-s relative to the 2-to-n pion scattering amplitudes. Finally, several plots of differential cross-sections for 2-to-2 pion scattering as a function of s and the scattering angle are obtained at fixed values of s and separately at fixed scattering angles, some of the predictions are compared to experimental data and phenomenological aspects are discussed.

The AdS3/CFT2 correspondence provides the best arena to test the holographic duality. This is because there is a better understanding of how to quantise strings on AdS3, compared with the higher dimensional cases, and the relative tractability of two-dimensional CFTs. In spite of this, little effort has been made to construct and classify supersymmetric AdS3 solutions. By making use of G-structure techniques, I will discuss AdS3 solutions to massive IIA realising a superconformal algebra osp(n|2) for n=5,6. In particular, the solutions that preserve N = (0, 6) supersymmetry involve a three-dimensional complex projective space in their internal geometry, and thus bear some resemblance with the ABJM/ABJ geometries. I will discuss that this resemblance becomes useful in the study of their dual CFTs.

The distance conjecture diagnoses viable low energy effective realisations of consistent theories of quantum gravity by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in parameter space are naturally intertwined with string dualities. We explore the implications of the distance conjecture when T-duality is applied to curved compact manifolds and in presence of (non-)geometric fluxes. We provide evidence to how divergent potentials signal pathological infinite distance points in the scalar field space where towers of light states cannot be sustained by the curved background. This leads us to suggest an extension to the current statement of the Swampland distance conjecture in curved spaces or in presence of non-trivial fluxes supporting the background.

The Swampland Cobordism Conjecture postulates that in any consistent theory of Quantum Gravity all cobordism classes must be trivial, $\Omega^{\text{QG}}_d=0$, as otherwise this would result in global symmetries. Dynamically, this is realized through the existence of Bubble of Nothing or End of the World Brane solutions mediating the decay of vacuum into nothing through the collapse of the internal geometry. While Witten’s original BoN construction features a circle compactification smoothly contracting into a point, one expects that the presence of a more rich internal structure or defects killing cobordism invariants results in more complicated solutions. We argue for the minimal intermediate topology changes that the compact manifold must go through before finally collapsing into nothing. This allows us to obtain information about the internal structure of “thick” BoN or EotW brane constructions (and their intersections) for general compactifications, as well as the location of the required defects. 

Six-dimensional superconformal field theories (SCFTs) have an atomic classification in terms of elementary building blocks, conformal systems that generalize matter and can be fused together to form all known 6d SCFTs in terms of generalized 6d quivers. It is therefore natural to ask whether 5d SCFTs can be organized in a similar manner, as the outcome of fusions of certain elementary building blocks, which we call 5d conformal matter theories. We explore this idea by giving a systematic construction of these irreducible "bifundamental" ADE SCFT building blocks, via geometric engineering techniques in M-theory. We then show how these can be gauged together giving rise to 5d SCFTs captured by 5d generalized linear quivers with ADE gauge groups as nodes, and links given by 5d conformal matter. As a bonus, this allows us to exhibit novel 5d dualities. Finally, to further characterize the 5d conformal matter SCFTs, we investigate their dimensional reduction to 4d, as well as their magnetic quivers.

Poster joint with Mario De Marco

One of the challenges of heterotic compactification on a Calabi-Yau threefold is to determine the physical (27)3 Yukawa couplings of the resulting four-dimensional N=1 theory. In general, the calculation necessitates knowledge of the Ricci-flat metric. However, in the standard embedding, which references the tangent bundle, we can compute normalized Yukawa couplings from the Weil-Petersson metric on the moduli space of complex structure deformations of the Calabi-Yau manifold. In various examples (the Fermat quintic, the intersection of two cubics in ℙ5, and the Tian-Yau manifold), we calculate the normalized Yukawa couplings for (2,1)-forms using the Weil-Petersson metric obtained from the Kodaira-Spencer map. In cases where h1,1=1, this is compared to a complementary calculation based on performing period integrals. A third expression for the normalized Yukawa couplings is obtained from a machine learned approximate Ricci-flat metric making use of explicit harmonic representatives. The excellent agreement between the different approaches opens the door to precision string phenomenology.

In six dimensions, there is an exotic N=(4,0) supermultiplet that contains only fields of spin ≤2, but no graviton, and that on a circle reduces to 5D N=4 supergravity. It has been proposed that, if suitable interactions exist, the (4,0) theory might provide a consistent alternative UV completion for N=4 5D supergravity, realizing a supersymmetric version of asymptotic safety. In this note we argue that any Lorentz-invariant (4,0) theory (interacting or not) carries an exact global symmetry when compactified on S1, and is therefore incompatible with the Swampland no global symmetries conjecture. Another example of exotic supergravity, the 6D (3,1) theory, does not have this problem. We study the general case and find that the only exotic spin-2 field that reduces to Einsteinian gravity and has no global symmetries when compactified on a high-dimensional torus is that of the (3,1) theory. All other possibilities either yield several gravitons or have global symmetries

The framework of tame geometry provides a way to quantify the geometric complexity of physical and mathematical quantities. We explore applications of this concept to various physical settings. Firstly, it provides a promising approach to understand the structure and complexity of the landscape of string theory vacua. In another application, we propose a method to quantify the complexity of an effective field theory and compare this to the complexity of the scattering amplitudes of the theory.

The Coulomb branch integral can be evaluated in 4D N=2 topologically twisted SYM, a.k.a. Donaldson--Witten (DW) theory, by integrating over the modular fundamental domain. This integral may diverge when the gauge coupling goes to imaginary infinity, therefore, we put forward a new prescription for the regularization of the fundamental domain and associated moduli space. Beyond evaluating the non-holomorphic correlation functions, we verify the universality of this regularization scheme in two examples. Firstly, in presence of a Kahler potential observable which introduces soft supersymmetry breaking, one can read off the phase transitions of the associated adjoint N=2 SQCD from the convergence and modular domains of correlation functions; Secondly, we restore the vacuum amplitude of one-loop closed string theory in a more efficient way with analytic expression obtained. Finally, we generalized our prescription to N=2* theory (DW theory with one pair of adjoint scalars). This poster is based on my ongoing work with Jan Manschot.