XVI Workshop on Geometric Correspondences of Gauge Theories

Jun 15, 2026, 9:00 AM → Jun 19, 2026, 6:00 PM Europe/Rome

Room D (iGAP)

The focus of the workshop is on recent developments in correspondences among supersymmetric gauge theories in various dimensions, topological field theories, 2D conformal field theories, integrable systems and the corresponding moduli spaces.

The Workshop is organized in the context of the Institute for Geometry and Physics.

Organizers F. Benini, M. Bershtein, G. Bonelli, T. Pedroni, G. Prieto-Varela, A. Tanzini

List of Speakers

• Ines Aniceto (Southampton University, UK)
• Alexandre Belin (Università Milano Bicocca)
• Anna Biggs (Princeton University) [zoom]
• Loic Bramley (Heriott Watt University)
• Pavlo Gavrylenko (Birmingham University)
• Luca Griguolo (Univ. Parma)
• Pietro Longhi (Uppsala Univ.)
• Andrey Marshakov (Skoltech - Moscow) 
• Tomoki Nosaka (SIMIS)
• Olga Papadoulaki (CPHT Paris)
• Tomas Prochazka (SEZNAM)
• Maria Rodriguez (Utah State University and Madrid, IFT)
• Lorenzo Ruggeri (Univ. Torino)
• Raoul Santachiara (LPTMS, Orsay, Paris)
• Chiara Toldo (Université Libre de Bruxelles) [zoom]
• Aleksandr Trufanov (Université de Montréal)
• Maxim Zabzine (Uppsala Univ.)

 

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The workshop is financially supported by IGAP, INFN and SISSA.

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Link to the 2011 edition website.  
Link to the 2012 edition website.  
Link to the 2013 edition website.  
Link to the 2015 edition website.  
Link to the 2016 edition website.  
Link to the 2017 edition website.  
Link to the 2018 edition website.  
Link to the 2019 edition website.  
Link to the 2020 edition website.  
Link to the 2021 edition website.  
Link to the 2022 edition website. 
Link to the 2023 edition website. 
Link to the 2024 edition website.
Link to the 2025 edition website.

 

     

Mon, June 15

1 On equivariant A and B-models

I will briefly discuss how to incorporate the world-sheet equivariance to A and B-models and how they can
be modified. I will discuss different features for equivariant B-model and some puzzles.

Speaker: Maxim Zabzine (Uppsala Univ.)

11:00 AM Break

2 Open strings on knot complements

This talk will report on recent developments at the intersection of QFT and low-dimensional topology. WRT invariants of 3-manifolds were conjectured by Gukov-Pei-Putrov-Vafa to admit a refinement and generalization known as Z-hat invariants, motivated by 3d-3d correspondence. In following work, Gukov and Manolescu introduced a generalization of Z-hat for knot complements. By the Lickorish-Wallance theorem these can be regarded as more fundamental building blocks for Z-hat of closed 3-manifolds, which can be recovered by surgery formulae. In this talk I will present a first-principles computation of the Gukov-Manolescu invariant for (2,2p+1) torus knots. The derivation is based on the duality between Chern-Simons gauge theory and A-model open topological strings, and hinges on a localization technique for counting holomorphic curves on the knot complement. The formula that we obtain corresponds to the open topological string partition function in the resolved conifold with a Lagrangian brane supported on the knot complement. The technique developed in this work applies more generally to all fibered knots. Based on joint works with S. Chauhan and T. Ekholm.

Speaker: Pietro Longhi (Uppsala Univ.)

12:30 PM Lunch

3 Riemann-Hilbert problems, Fredholm determinants and connection formulas for the q-Painlevé III₃ tau functions

q-Painlevé III₃ equation is related to the N=1 5d gauge theory. We reformulate its linear problem as the Riemann-Hilbert problem on a circle. Then, we express its tau function as the Fredholm determinant related to this Riemann-Hilbert problem. This expression allows us to study the global properties of the q-Painlevé solution, and so of the partition function of the 5d gauge theory. The talk will be based on https://arxiv.org/abs/2501.01419.

Speaker: Pavlo Gavrylenko (Birmingham University)

3:30 PM Break

4 Confining strings and N=2 black holes

I consider a non-common type of 4D/2D correspondence, which allows to compute the confining spectrum of 4D supersymmetric QCD by means of 2D superconformal world-sheet theory, corresponding to N=2 supersymmetric version of 2D black hole. Amazingly enough, both Kahler and complex deformations of the world-sheet theory affect only the number of states in 4D. The conjecture survives under few tests on state's counting, reduced on field theory side to certain exercises in representation theory.

Speaker: Andrey Marshakov (Skoltech - Moscow)

Tue, June 16

5 Fortuity and BPS state counting in ABJM

The fortuitous mechanism is a way to distinguish different type of microstates in quantum gravity. For BPS states, the question can be made sharp: fortuitous operators are the true black hole microstates and display an erratic N-dependence. A given operator built out of the fundamental fields of the theory can be BPS at some value of N, while at higher N the same operator fails to be BPS due to a trace relation disappearing. On the other hand, monotone operators correspond to excitations of the (BPS) bulk perturbative fields, and a given monotone operator built out of the fundamental fields remains BPS at all N. In this talk, I explore this mechanism in ABJM theory, which has several features absent in the canonical example of N=4 SYM: a non-continuous coupling, and non-perturbative sectors coming from monopole operators. I will perform a systematic analysis of the operators of the theory at low quantum numbers in ABJM at N=2, finding the first fortuitous operators. I will work both at large k, in direct comparison to what is done in N=4 SYM, but also at small k where monopole operators become important. Finally, I will speculate on a microscopic origin of the N^(3/2) scaling of the BH entropy and its connection to fortuity.

Speaker: Alexandre Belin (Università Milano Bicocca)

11:00 AM Break

6 W-algebras and ODE/IM

I want to talk about results obtained recently with Matej Kudrna in the context of ODE/IM (or ODE/IQFT) correspondence for WN algebras. WN algebras are VOAs that are natural generalizations of Virasoro algebra. They have interesting integrable structures, in particular the quantum KP hierarchy (which generalizes the quantum KdV hierarchy in the case of Virasoro). The simultaneous eigenvalues of infinite family of local conserved charges are diagonalized by Bethe equations and can be mapped via ODE/IM correspondence to ordinary differential operators in the complex plane (opers).

Speaker: Tomas Prochazka (SEZNAM)

12:30 PM Lunch

7 AGT for Toric Surfaces

Via AGT, observables of Pestun's 4d N=2 gauge theories on S^4 are known to reproduce correlators in Liouville theory. A natural question is whether a similar correspondence assigns a two-dimensional CFT to Pestun-like theories on more general compact four-manifolds. In this talk, I will answer this question affirmatively for a large class of compact toric manifolds. As a concrete example, I will show how the partition function on F_0 reproduces a four-point function in Liouville gravity. I will also discuss how four-point functions with one degenerate insertion are reproduced by the insertion of codimension two defects on F_0. Finally, I will consider general Hirzebruch surfaces and toric surfaces with more than four fixed points.

Speaker: Lorenzo Ruggeri (Univ. Torino)

3:30 PM Break

Wed, June 17

8 Non compact Imaginary Liouville Theory

We propose a path integral definiton of a CFT that extends the imaginary Liouville theory based on a compactified boson and which provides non vanishing corrélation functions when Coulomb has neutrality condition is not satisfied.

Speaker: Raoul Santachiara (LPTMS, Orsay, Paris)

11:00 AM Break

9 Affine Laumon Spaces and Admissible Representations of affine gl(n)

Affine Laumon spaces arise as moduli spaces of (SU(N)) instantons in the presence of a surface operator. Their equivariant cohomology was shown to form a Verma module over affine gl(n) for generic equivariant parameters. The torus fixed points provide a natural basis, which may be viewed as an affine analogue of the Gelfand--Tsetlin basis. We study a specialization of the equivariant parameters corresponding to a dominant, not necessarily integral, highest weight. In this case, the compact components of the fixed-point set are isolated points. We show that these points form a basis of an irreducible highest-weight module. In particular, this gives a combinatorial realization of admissible modules. On the level of characters, our construction provides a combinatorial interpretation of the Kac--Wakimoto character formula, generalizing the relation between semistandard Young tableaux and the Weyl character formula for Schur polynomials. This talk is based on joint work in progress with M. Bershtein, E. Mukhin, and L. Rybnikov.

Speaker: Aleksandr Trufanov (Université de Montréal)

12:30 PM Lunch

10 Representation theory of line operators in 4d HT QFTs

Line operators in a 4d holomorphic-topological theory assemble into a meromorphic braided tensor category. Using boundary conditions, one can engineer a fibre functor on such a category, and perform categorical reconstruction to extract a vertex quantum group, for which line operators are modules. Such algebras will have the structure of a 'chiral (relative) Drinfeld double'. For 4d N=2 theories in the HT-twist, we conjecturally recover the relevant cohomological Hall algebra as the positive half of what we call a 'BPS Yangian', which for simple examples we explicitly construct out of BPS states. Moreover, every algebra will come with a collection of chiral coproducts / R-matrices and Drinfeld twists between them. In turn, we obtain a physical interpretation of Drinfeld-deformed-type coproducts. This talk is based on joint work with Tudor Dimofte.

Speaker: Loic Bramley (Heriott Watt University)

3:30 PM Break

11 A melonic quantum mechanical model without disorder

I will describe a quantum mechanical model involving N interacting fermions without disorder that has a large N melonic expansion. In particular, it has the same Schwinger-Dyson equations and low energy physics as the \mathcal{N} = 2 supersymmetric SYK model. The model is SU(2) invariant, and the supercharge involves the SU(2) 3j symbol. I will conceptually explain why the model has a melonic expansion, discuss various solvable corners, and present some results of exact diagonalization for small values of N. Expanded around states with maximal angular momentum, the model is approximated by a two dimensional CFT. The BPS states have a simple description in that regime. Based on arXiv:2601.08908 with L. Lin and J. Maldacena.

Speaker: Anna Biggs (Princeton University)

Thu, June 18

12 Constructing composite black hole objects in 5d

I will review the construction of composite black hole objects in 5d via blackfolds and D-brane probes and comment on their relevance for holography. I will show how to construct novel generic Black Rings and Black Saturns in 5d Minkowski and Anti-de Sitter space, and comment on their thermodynamics and supersymmetry properties. I will also comment on the stability of wrapped D-branes on AdS5 black holes with uplift in II B string theory, and their relation to Grey Galaxies and Dual Dressed Giant Gravitons.

Speaker: Chiara Toldo (Université Libre de Bruxelles)

11:00 AM Break

13 Quantum Corrections Near Extremality for AdS and flat asymptotics

In the first part of this talk, I will present how quantum corrections stemming from the $NAdS_{2}$ region of the near extremal 4-dimensional Reissner–Nordström (RN) asymptotically AdS black brane change the behaviour of the retarded Green’s function holographically and what are the implications for the shear viscosity ($\eta$) and the bound of its ratio with the entropy density (s) ($\eta/s$).
In the second part, I will present how quantum corrections stemming from the $NAdS_{2}$ region of the near extremal 4-dimensional asymptotically flat RN black hole, change its superradiance properties as well as the cross-section of charged scalars.
I will conclude with some future directions.

Speaker: Olga Papadoulaki (CPHT Paris)

12:30 PM Lunch

14 Machine-Learning and Love Numbers

Tidal Love numbers characterize how compact objects respond to external gravitational fields. In this talk I will discuss a machine-learning approach to compute Love numbers directly from the perturbation equations. I will present some results and comment on how this connects to more traditional approaches in black hole perturbation theory.

Speaker: Maria Rodriguez (Utah State University and Madrid, IFT)

3:30 PM Break

15 Analytic approaches to perturbations of strongly coupled Yang-Mills plasma

In this talk I will study perturbations of Yang-Mills plasma, represented by scalar quasi-
normal modes of AdS black branes, as functions of the wave number q . This will be done using a combination of Seiberg-Witten and exact WKB approaches. The instanton expansion naturally provides an analytic understanding of the validity of the classical spectral methods based on the truncation of the boundary value problem. I will then show that a large wave number asymptotic analysis based on exact WKB provides an alternative description that remains accurate far beyond the strict large-q regime, and that can be analytically continued in the entire range of q from zero to infinity.

Speaker: Ines Aniceto (Southampton University, UK)

Fri, June 19

16 The fate of the flux tube in presence of a large R-charge

This talk explores the fate of the "confining" N=4 flux tube in the presence of a large R-charge.
Using the AdS/CFT correspondence, we examine how inserting this charge induces a non-analytic transition.
The flux tube loses its standard configuration, evolving into a highly excited, "deconfined" state.
We map this regime to the BMN limit and integrable open spin chains with reflecting boundaries.
Finally, we compute the generalized cusp anomalous dimension across all coupling regimes.

Speaker: Luca Griguolo (Univ. Parma)

11:00 AM Break

17 New recursion relations for M2-brane matrix models

We study the finite dimensional integrals which calculate the sphere partition function of the theories of N M2-branes, which we shall call M2-matrix models. M2-matrix models has been studied in detail in particular for the U(N)k x U(N+M){-k} ABJ(M) theory, where it was found that the generating function of the matrix models obey the Hirota bilinear form of the q-discrete Painleve III_3 equation. We find similar bilinear relations also hold in more general setups. Furthermore, combining the bilinear relations with the duality in 3d gauge theory we find simple recursion relation with respect to N, which is a new powerful tool to study the finite N corrections in M2-matrix models.

Speaker: Tomoki Nosaka (SIMIS)

18 Final discussion