Talks and abstracts

Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to dualities via the procedure of half-space gauging. In this talk I will discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. Our approach allows us to include target spaces without non-trivial 1-cycles, does not require the NLSM to be conformal, and when it is conformal it does not need to be rational; moreover, it highlights the microscopic origin of the topological terms that are responsible for the non-invertibility of the defect. An interesting class of examples are Wess-Zumino-Witten models, which are self-dual under a discrete gauging of a subgroup of the isometry symmetry and so host a topological defect line with Tambara-Yamagami fusion. Time permitting, I will also discuss the target space interpretation of those defects as well as implications for String Theory. 

We discuss D=10 D0-brane and multiple D0-brane (mD0) system in classical and quantum domain. Despite the D0-brane quantization was discussed before in the literature, neither its quantum state spectrum nor its field theory were elaborated. We obtain these from the first quantization of D0-brane model in its spinor moving frame formulation. The choice of this formulation allowed us to find the D0-brane quantum state spectrum in terms of the 10D generalization of the spinor helicity formalism  and so-called on-shell superfields providing a basis for superamplitude formalism for D0-branes. Furthermore, this provides the basis for quantization and constructung the field theory of multiple-D0-brane system on the basis of its complete supersymmetric action known presently in spinor moving frame formulation only. We briefly discuss this action as well as the progress towards the mD0 field theory and the simplest (super)amplitudes of type IIA string theory involving D0-brane and supergravitons. 

In this talk I will introduce the notion of superconformal defects and I will discuss a non-trivial relation between two important observables: the stress tensor one-point function, related to deformations of the geometry and the displacement norm, related to shape deformation. This relation, which we recently proved, shows that supersymmetry identifies two natural notions of brane tension in Anti-de Sitter gravity. As a byproduct, we show that a modification of the energy-momentum tensor that removes the stress of static superconformal defects, ensures also that the radiation these emit obeys the Null Energy Condition. 

In this talk I will introduce the holomorphic twist of 4d N=1 SQFTs, explain how this sector is governed by a higher dimensional analogue of a vertex operator algebra and most importantly show which kind of observables can be extracted from this framework. In particular, I will show how anomalies are encoded, how the holomorphic twist provides a refined framework to test for supersymmetry enhancement and how the associated VOA of N=2 SCFTs can be recovered from this framework. 

I will present a recently derived conformal dispersion relation that allows to compute the four-point function of operators inserted on a conformal line defect as an integral over its double discontinuity. As an application of this formula, I will discuss its use in evaluating holographic correlators defined on the half-BPS Wilson line in planar N=4 super Yang-Mills. 

As explained in the work of Alba, Fateev, Litvinov and Tarnopolskiy (AFLT), the AGT conjecture implies the existence of a special basis in the (q-deformed) CFT Fock space which matches the instanton expansion of the corresponding 5d Nekrasov partition functions. After bosonization, this basis of AFLT states coincides with the basis of generalized Macdonald polynomials, which are associated to the classes of fixed points in the equivariant K-theory of instanton moduli spaces. In this talk, I will provide a new algebraic formula for AFLT states of arbitrary rank constructed out of the intertwiners of the quantum toroidal gl_1 algebra. In the case of rank r=1, this recovers an old identity of Garsia, Haiman and Tesler for ordinary Macdonald functions. 

We investigate integrability properties of Gukov-Witten 1/2-BPS surface defects in SU(N) N=4 super-Yang-Mills (SYM) theory in the large-N limit. We demonstrate that ordinary Gukov-Witten defects, which depend on a set of continuous parameters, are not integrable except for special sub-sectors. In contrast to these, we show that rigid Gukov-Witten defects, which depend on a discrete parameter but not on continuous ones, appear integrable in a corner of the discrete parameter space. Whenever we find an integrable sector, we derive a closed-form factorised expression for the leading-order one-point function of unprotected operators built out of the adjoint scalars of N = 4 SYM theory. Our results raise the possibility of finding an all-loop formula for one-point functions of unprotected operators in the presence of a rigid Gukov-Witten defect at the corner in parameter space. 

We consider dynamics of ensembles of geodesics in Lin-Lunin-Maldacena (LLM) geometries, first black and white and then grayscale (coarse-grained). Ensemble averaging over geodesics converges to an "average" geodesic which on long timescales coincides with the geodesic in grayscale geometries. The same conclusion holds accordingly also for the two-point functions of the dual CFT in the eikonal regime. We then cosider LLM-like black hole solutions and compare them to the outcome of LLM averaging. All of this suggests that we might understand black holes as averages over microstate solutions. 

The Euclidean on-shell action (OSA) of supersymmetric saddles of supergravity theories in AdS is an important object in holography. It can be viewed as the grand canonical entropy function. In explicit examples it has been observed that it only depends on topological data: the fugacities that ``dress'' the dual supersymmetric index. Recently, there has been a flurry of activity in employing the machinery of equivariant localization in supergravity to show that indeed the OSA can be obtained in a metric-agnostic fashion. Technically these advancements have been limited to even-dimensional supergravities.

I will present a localization formula that can be used to calculate, in an entirely topological manner, the OSA in supergravity theories in AdS_d with d odd. I will discuss the subtle interplay between boundary terms in the process of renormalisation. Then, I will specify to 5d minimal supergravity and show how the famous result for the large-N superconformal index of 4d SCFT’s with an R-symmetry can be recovered using our technique. Finally, I will discuss generalisations to different topologies.

This talk investigates the reformulation of knot and link invariants as correlation functions in unitary matrix models, within the framework of Chern-Simons theory. In the double-scaling limit with fixed ’t Hooft coupling, Wilson loop operators simplify to trace insertions, enabling a systematic large N expansion of correlators. Leading and subleading contributions, structured through connected correlators, distinguish topological configurations and encode the interaction content of knot and link observables. Focusing on the Labastida–Marino–Ooguri–Vafa (LMOV) invariants, we analyze their generating function and compute the large N behavior of its coefficients, demonstrating that connected correlators contribute to key terms and reveal the asymptotic structure of the LMOV invariants. 

The topological string/spectral theory correspondence establishes a precise, non-perturbative duality between topological strings on local Calabi-Yau threefolds and the spectral theory of quantized mirror curves. This duality has been rigorously formulated for the closed string sector, but the open string sector is less understood. In this talk, I will explain how one can use open string partition functions to construct true eigenfunctions for the quantized mirror curve of local F0. 

Extended operators in Quantum Field Theory exhibit rich and nontrivial dynamics, describing a variety of physical phenomena. These systems often involve strong coupling at long distances, where the interaction between the bulk and defects makes analytical studies challenging. In this talk, I will discuss how the behavior of bulk symmetries in the presence of co-dimension one defects (or generically interfaces) can strongly constrain their dynamics. In particular, I will introduce new RG-invariant quantities that can be tracked along the defect RG flow and used to make predictions about the possible IR behavior of such extended defects. Finally I will also show how hidden symmetries, which are not present in the bulk theory, can be used to produce non-trivial defect conformal manifolds and determine their properties. 

We introduce a novel functional approach to quantum field theory, which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with all the traditional importance sampling protocols well-defined only for imaginary time. Our novel importance sampling procedure is realized by means of a deterministic dynamics generated by Hamilton-like equations evolving with respect to an auxiliary time parameter $\tau$. We show that the microcanonical correlation functions are equivalent to those generated by a Minkowskian canonical theory where quantum fields fluctuations are weighted by the factor $exp(iS/hbar)$, $S$ being the original action of the system. Alongside the above analytical evidence, we performed numerical tests that validate our approach in the case of the quantum oscillator and the free scalar field theory. 

In this talk we study the large charge sector of N=4 Super Yang-Mills (SYM) with SU(N) gauge group by constructing a special class of half-BPS heavy operators, termed "canonical operators". In the large-charge 't Hooft limit canonical operator insertions map N=4 SYM onto the Coulomb branch by assigning a classical profile to the scalar fields with non-vanishing values along the diagonals given by the roots of unity. We follow a semiclassical approach to study two-point, three-point and Heavy-Heavy-Light-Light (HHLL) correlators, and provide consistent evidence of our findings by computing the same observables via supersymmetric localization. 

Three-dimensional N=4 superconformal field theories (SCFTs) admit a specific type of deformation, known as universal mass deformation, which originates from the stress tensor multiplet and is therefore present in all 3d N=4 SCFTs. It has been argued that this deformation modifies the supersymmetry algebra and leads to a fully gapped theory in the infrared (IR). In this work, we analyze the universal mass deformation of general Abelian 3d N=4 SCFTs and show that the resulting gapped phase is described by an Abelian topological quantum field theory (TQFT). Furthermore, we prove that two Abelian 3d N=4 SCFTs related by mirror symmetry give rise to TQFTs that are connected through a generalized form of level-rank duality. In the case of self-mirror symmetric SCFTs, we demonstrate that the resulting TQFT exhibits time-reversal invariance. Since the universal mass deformation is expected to preserve both symmetries and anomalies, we explicitly verify ’t Hooft anomaly matching in the example of supersymmetric quantum electrodynamics (SQED). 

Knot-quiver correspondence provided a picture of BPS state counts in 3d N=2 theories associated to symmetric quivers. On the other hand, we have another, well established construction of BPS states in 4d N=2 theories which also correspond to quivers, but not symmetric ones. The aim of this talk is to give an answer for an obvious and long-standing question about the relation between these two perspectives. 

Soft theorems in Quantum Field Theory, namely the factorization of a scattering amplitude when one of the degrees of freedom carries a small amount of energy, are known to be related to Lorentz symmetry. Here we explore this connection in the context of BFSS matrix theory, a matrix quantum mechanics theory which is conjectured to be dual to eleven-dimensional supergravity in the low energy limit. We show that, in this limit, the theory admits vertex operators with the correct quantum numbers to represent supergravitons in target space and such that their correlation functions exhibit soft factorization at both leading and subleading order. Hence, we leverage the connection between Soft Theorems and Lorentz invariance to conclude that the theory enjoys full eleven-dimensional Lorentz symmetry. This result serves as a crucial argument in favour of the above conjecture. 

I will talk about the recent progress with black hole operators in the supersymmetric gauge theories, mostly the N=4 Super-Yang-Mills. The goal is to identify supercharge cohomologies of the weakly coupled SYM theory with finite-rank gauge groups, as holographic incarnation of the supersymmetric AdS black hole microstates. We present infinite towers of black hole (fortuitous) operators in the N=4 SYM with the smallest non-trivial gauge groups SU(2) and SU(3), and establish systematic arguments for their fortuity, i.e. they are not part of the supergraviton spectrum. We also extract gravitational features from the microscopic operators, namely that black holes may be dressed by graviton hair with large angular momenta or be wrapped by branes with large charges, resulting in the brane-fused black hole operators.

Resurgence and trans-series techniques provide a powerful framework for understanding non-perturbative phenomena in quantum field theory and beyond. In this talk, I will present a complete trans-series solution for key observables in the Lieb-Liniger model, a prototypical integrable system in one dimension. The trans-series is explicitly constructed from a perturbative basis derived via ordinary differential equations and is shown to satisfy non-trivial consistency conditions. Furthermore, high-precision numerical results demonstrate its consistency. These results highlight the trans-series structure in integrable QFTs and its relevance to related models.

We study the 2D fermionic SYK model with Majorana fermions, featuring a kinetic term with a quartic expression and a $2q$-body interaction with Gaussian disorder. By minimizing the effective action or solving the SD equation for $q=1$, we determine that the appropriate ansatz involves zero spins. Our computation of the Lyapunov exponent shows violations of chaos and unitarity bounds. The gravitational dual corresponds to AdS$_3$ Einstein gravity with a finite radial cut-off even if we lose the non-zero spins. We also extend the SYK model to higher dimensions while maintaining a similar SD equation in the IR. 

I'll discuss the superconformal index of N=4 SU(N) super Yang-Mills and its holographic interpretation as the partition function of type IIB string theory on AdS_5 x S^5. The latter contains various gravitational saddles, such as Euclidean black holes and orbifolds thereof. It also contains saddles with various SUSY branes on top of these backgrounds. I will identify these contributions within the superconformal index and explain the origin of the branes both in a Cardy-like limit (as eigenvalue instantons) and at large N (as certain continuous solutions in the Bethe Ansatz approach). This understanding allows us to suggest a connection between the branes and the orbifolds, and to better explain the phase diagram of the theory. 

We study solutions of q-Virasoro constraints in refined, also knowm as (q,t)-deformed, matrix models with various potentials. Our goal is to establish an analogue of the W (or cut-and-joint) representation and its relation to "superintegrability"—a special form of averages of Macdonald polynomials. The examples considered come from localization of 3D SUSY theories, including the refined Chern-Simons model and gauge theories with adjoint and fundamental matter. We show that these models are governed by certain recursion relations given by a quantum toroidal algebra, also known as the Ding-Iohara-Miki (DIM) algebra or the elliptic Hall algebra. For the Chern-Simons model at q=t these recursions seem to reproduce the recently obtained skein recursion relations for the unknot. 

In this talk, I will present the approach of Operator Product Expansion (OPE) Algebras to introduce models of quantum fields. This is a generalization of the theory of vertex algebras that has been successfully applied in two-dimensional conformal field theory. 

We will discuss a physically motivated correspondence between the two most famous combinatorial polytopes. The quantum dilogarithm function will play a key role in this connection. 

Integrable quantum field theories provide a framework for describing strongly correlated systems using a (quasi)-particle picture that is reminiscent of weakly coupled theories. This approach has led to the development of powerful analytical tools, such as the S-matrix and vacuum form-factor bootstrap programs. Recently, there has been renewed interest in understanding non-equilibrium quantum dynamics, where finite energy density states are typically probed. This necessitates the development of new tools and techniques. In this talk, I will present the thermodynamic form-factors bootstrap program, which extends the vacuum bootstrap to situations involving excitations relative to finite energy states, rather than the vacuum. I will outline the structure of this program and discuss results for dynamical correlation functions at finite temperatures and in non-equilibrium steady states. Additionally, the program offers insights into more general results for quantum field theories such as crossing symmetry in the absence of Lorentz invariance. 

The  Hilbert space for the Haldane spherical model are endowed with a structure of the massless ladder $SU(2,2)$-representation. The Landau levels are mapped by duality to the quantum Kepler model, that is, the hydrogen atom or more generally the MIC-Kepler system.  The inherent $AdS_5$ geometry of  the MIC-Kepler system is discussed. 

The AdS3/CFT2 correspondence provides an exceptional framework to explore holography, as string quantization on AdS3 is better understood than in higher-dimensional cases, and two-dimensional CFTs offer a relatively tractable setting. Despite these advantages, the systematic construction and classification of supersymmetric AdS3 solutions remain largely unexplored. In this talk, I will present new AdS3 solutions to massive IIA supergravity, which realize the superconformal algebra osp(n|2) for n=5,6. In particular, I will focus on solutions preserving  N=(0,6) supersymmetry, whose internal geometry features a three-dimensional complex projective space, reminiscent of the ABJM/ABJ backgrounds. This resemblance provides valuable insight into the structure of their dual CFTs, shedding light on their field-theoretic interpretation. Additionally, I will discuss AdS3 solutions with N=(0,2) supersymmetry obtained through deformations of the N=(0,6) case. 

I will present how a strongly coupled inhomogeneous phase of the Gross-Neveu model appears as non-perturbative effects at weak coupling. By turning on a chemical potential to a subset of fermion in the O(2N) Gross-Neveu model, we discover that at large N bound states coalesce in a "crystal". This phase is characterised by two new dynamically generated scales that show up in perturbation theory as exotic renormalon effects. Through integrability, these non-perturbative effects can be understood exactly at finite N.

We propose Abelian mirror duals for 3d Chern-Simons SQCD theories. We test these dualities by analyzing supersymmetric partition functions and their consistency under mass deformations. We discuss the implications of these dualities, including the enhancement of topological symmetry and the presence of moduli spaces of vacua in certain SQCD theories.

Following recent studies on black hole solutions with horizons containing orbifold singularities, an understanding of SQFTs on the singular boundaries is needed. In this talk, based on 2502.13611, building on a previous identification of theories on orbifolds with gauge theories on smooth spaces with Gukov-Witten defects I will propose a refinement which makes use of so called twist defects. The combined effect of the two defects makes the fields multivalued when going around the singularity. This equivalent description reproduces the spindle index computed employing the orbifold equivariant index and it motivates an equivalence between partition functions on spaces with surplus and deficit angles observed in 2404.11600. 

Recently, we computed the  generating functional of Euclidean asymptotic correlators at short-distance of single-trace twist-2 operators in large-N SU(N) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one arising from the spin-statistics theorem for the glueballs. To solve the sign puzzle, we reconsider the proof that in 't Hooft large-N expansion of YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of n-punctured tori. We discover that for twist-2 operators it contains -- in addition to the n-punctured tori -- the normalization of tori with p pinches and n-p punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Besides, the new sector contributes trivially to the nonperturbative S matrix because -- for example -- the n-pinched torus represents nonperturbatively a loop of n glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing S matrix. 

Supersymmetric quantum field theories (SQFTs) with eight supercharges in dimensions 3 to 6 feature rich moduli spaces, where the Higgs branches - often singular hyper-Kähler spaces - play a central role. The framework of magnetic quivers provides a combinatorial tool to fully encode these geometries, while the decay and fission algorithm efficiently determines their phase structure and renormalization group (RG) flows through convex linear algebra techniques.

In this talk, I will present a unified perspective on Higgs branches and RG flows in SCFTs across dimensions 3 to 6, focusing in particular on recent advances for three-dimensional N=3 Chern-Simons matter (CSM) theories. Utilizing Type IIB brane constructions, we derive magnetic quivers that capture the maximal hyper-Kähler branches of both N=3 and N=4 CSM theories, including cases with non-trivial Chern-Simons levels beyond the reach of standard dualities. This provides the first systematic characterization of their moduli spaces and RG flows, expanding the magnetic quiver technology into new, previously unexplored territory.

Based primarily on recent work with F. Marino (arXiv:2503.02744), building on earlier developments with A. Bourget and Z. Zhong (arXiv:2312.05304, 2401.08757). 

We present a full Batalin-Vilkovisky formulation of N=1 D=10 supergravity coupled to Yang-Mills multiplets, in the background independent component field formalism coming from generalised geometry. This is a joint work with Julian Kupka and Charles Strickland-Constable. 

In this talk I will discuss a proposal uplifting the background field formalism for the worldsheet to M2-branes. The associated generating functional is then evaluated at long wavelengths in which case it decomposes into a sum over saddles comprising of degenerate and non-degenerate M2-branes. The non-degenerate branes are explicitly quantised in well known holographic backgrounds and I discuss how the resulting integrals over zero-mode sectors get localised according to space-time supersymmetry. Finally, I will discuss how observables associated to these quantum M2-branes require a subtle choice of ensemble in holography, when compared to the dual field theory.