XV Workshop on Geometric Correspondences of Gauge Theories

Jun 16, 2025, 9:00 AM → Jun 20, 2025, 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.

Public transport strike on Friday June 20th

Busses will be guaranteed just from 6:00 to 9:00 and 13:00 to 16:00

Guaranteed trains:

• long distance 
• local

 

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

Organizers G. Bonelli, P. Gavrylenko, I. Majtara, T. Pedroni and A. Tanzini.

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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

 

Monday, June 16

1 Strings and near-extremal black holes in AdS3

I will describe features of superstring theory in AdS3 backgrounds. I will outline how the one-loop partition function reproduces the supergravity spectrum (in the semiclassical limit) and encodes the boundary supergravitons. Of particular interest will the regime where the AdS curvature is at the string scale, which we will be able to access within the conventional RNS formalism in one example. I will explain that how the tensionless string discussed in the literature differs from the one obtained by taking a suitable limit of our construction, and explain the origin of this difference. Finally, I will describe how the string partition function can be used to understand the thermodynamics of near-extremal BTZ black holes, and in particular recover the BPS index in an appropriate limit.

Speaker: Mukund Rangamani

11:00 AM Break

2 Toldo

12:30 PM Lunch

3 Emparan

3:30 PM Break

4 Discussion session

Tuesday, June 17

5 Periodic dilaton gravity and double-scaled SYK

I will discuss 2d dilaton gravity theories with a periodic potential. The periodicity implies a symmetry under discrete shifts in the momentum conjugate to the length of geodesic slices. This symmetry is to be gauged and discretizes the geodesic lengths. Moreover, lengths below a certain threshold become null states. Because of these, the entropy deviates drastically from the semiclassical Bekenstein-Hawking result. I will pay special attention to sine-dilaton gravity, which is holographically dual to double-scaled SYK, and for which I will discuss two limiting dualities: one between flat space quantum gravity and the Heisenberg algebra, and one between topological gravity and the Gaussian matrix integral.

Speaker: Parmentier

11:00 AM Break

6 Black holes, microstates and the Heun equation

Speaker: Rodolfo Russo

12:30 PM Lunch

7 Large charge meets semiclassics in N=4 Super Yang-Mills

In this talk we discuss 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.

Speaker: Cristoforo Iossa

3:30 PM Break

8 Irregular Kac-Moody representations, KZ-equations and Gaiotto-Teschner modules

In this talk, I will present irregular representations of Kac-Moody algebras where we restrict ourselves to the sl(2,C) case. I show how such irregular representations correspond to irregular Gaiotto-Teschner representations of the Virasoro algebra. The associated KZ equations for conformal blocks with one irregular operator at infinity and their integral representations are derived. By connecting to 2d Liouville theory, I will show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres-Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve.

Speaker: Babak Haghighat

Wednesday, June 18

9 Zabzine

11:00 AM Break

10 The skein-valued mirror of the topological vertex

Observables of the A-model open topological string encode counts of holomorphic curves with Lagrangian boundary conditions. When Lagrangian A-branes have non-compact support, the count of open holomorphic curves depends on the asymptotic geometry of Lagrangians at infinity. In this talk I will show how the asymptotic geometry of three Legendrian tori in contact S^5 encodes a set of equations whose solutions include the topological vertex, and its analytic continuation to other large volume regions in the moduli space of three toric branes in C^3. Based on joint works with Ekholm-Nakamura, and Ekholm-Shende.

Speaker: Longhi

12:30 PM Lunch

11 Probabilistic conformal blocks, their semi-classical limit and consequences.

The mathematically rigorous study of Conformal Field Theory (CFT) has recently attracted significant attention, driven by developments in probability theory. In this talk, I will present a probabilistic framework for defining conformal blocks on the one-point torus, along with the motivations underlying this approach. I will then discuss methods for analysing the (semi-)classical conformal block and its connection to the Lamé equation. Finally, I will briefly outline further results one can obtain from the (semi-)classical conformal blocks such as the Nekrasov–Rosly–Shatashvili (NRS) formula.

Speaker: Harini Desiraju

3:30 PM Break

12 Del Zotto

Thursday, June 19

13 Sine dilaton gravity: wormholes, finite matrices and q-holography

I will discuss a two-dimensional dilaton gravity theory with a sine potential. At the disk level, this theory admits a microscopic holographic realization as the double-scaled SYK model. Remarkably, in the open channel canonical quantization of the theory, the momentum conjugate to the length of two-sided Cauchy slices becomes periodic. As a result, the ERB length in sine dilaton gravity is discretized upon gauging this symmetry. For closed Cauchy slices, a similar discretization occurs in the physical Hilbert space, corresponding to a discrete spectrum for the length of the necks of trumpet geometries. By appropriately gluing two such trumpets together, one can then construct a wormhole geometry in sine dilaton gravity whose amplitude matches the spectral correlation functions of a one-cut matrix integral. This correspondence suggests that the theory provides a path integral formulation of q-deformed JT gravity, where the matrix size is large but finite, thus going beyond the regime of the double-scaled SYK model. Finally, I will describe how this theory of gravity can be regarded as a realization of q-deformed holography and propose a possible implementation of this framework to study the near-horizon dynamics of near-extremal de Sitter black holes.

Speaker: Jacopo Papalini

11:00 AM Break

14 Mazzocco

12:30 PM Lunch

15 Aniceto

3:30 PM Break

16 Integrability, gauge, black holes theories: their correspondences at work

Speaker: Davide Fioravanti

Friday, June 20

17 Many-faced Painlevé I

I will discuss an algebraic construction of irregular Virasoro conformal blocks describing the tau function of the first Painlevé equation, and explain how these quantities are related to topological recursion and holomorphic anomaly equation.

Speaker: Lisovyi

11:00 AM Break

18 Exact WKB of solutions by Borel summation and open TBA

I will present two exact WKB methods for solutions of differential equations within the framework of the differential equation/4d N=2 supersymmetric theory correspondence. The first method is the well-known Borel summation. I will demonstrate how supersymmetric theories provide a prescription for identifying the singularities on the Borel plane, as well as for formulating the associated discontinuities in the Borel summation. I will also introduce the Gaiotto–Moore–Neitzke (GMN) open TBA equations—integral equations whose solutions are closely related to those of the differential equations. And I will describe how to match the results from the two exact WKB methods.

Speaker: Qianyu Hao

19 Final discussion