New Trends in Non-Perturbative Gauge/String Theory and Integrability

Contribution List

29. Diagrammatic Expansion of Non-perturbative Little String Free Energies

Stefan Hohenegger (Lyon)

6/27/22, 10:00 AM

Diagrammatic Expansion of Non-perturbative Little String Free Energies
Abstract: In this talk I discuss the non-perturbative free energy of a class of Little String Theories of A-type, which are engineered by N parallel M5-branes on a circle. Exploiting non-perturbative symmetries of these theories, I provide evidence to leading instanton order (from the perspective of the low energy U(N)...

43. Random partitions and gauge group integrals: recent results

Souradeep Purkayastha (IMB)

6/27/22, 11:00 AM

Random matrix integrals have a natural connection with the Schur measure on random partitions. In this talk I briefly highlight recent work in this direction, in particular focusing on a generalization of the Gross-Witten-Wadia model to classical gauge groups.

28. What can little strings teach us about the geometric Langlands program?

Nathan Haouzi (IAS)

6/27/22, 11:50 AM

In its simplest incarnation, the geometric Langlands program was defined by Beilinson and Drinfeld in the late 90’s as relating, on one side, a flat connection on a Riemann surface, and on the other side, a more sophisticated structure known as a D-module. Since its inception, this conjectured correspondence has been a highly active and fruitful topic of research both for mathematicians and...

23. Shifted quantum groups and matter multiplets in supersymmetric gauge theories

Jean-Emile Bourgine (Melbourne)

6/27/22, 2:00 PM

39. Non-semisimple TQFTs and BPS q-series

Pavel Putrov (ICTP)

6/28/22, 9:30 AM

In my talk I will describe a relation between the 3d Topological Quantum Field Theories (TQFTs) of Blanchet--Costantino--Geer--Patureau-Mirand, constructed from a non-semisimple category of representations of a quantum group, and counting of BPS states in a 6d (2,0) superconformal field theory compactified on a 3-manifold with a topological twist.

30. Black hole perturbations from Liouville correlators

Cristoforo Iossa (SISSA)

6/28/22, 10:30 AM

Reversing the logic of the bootstrap approach in Liouville CFT we explicitly compute the connection formulae for degenerate conformal blocks. In the semiclassical limit of the theory, this amounts to solving the connection problem of Fuchsian ODEs. Generalizing to irregular insertions we solve as well for various confluences. Concentrating on the Heun equations, we can solve the wave equations...

22. Factorizability of the partition function of the supermatrix model

Nicolas Babinet (IMB)

6/28/22, 11:00 AM

In this talk we will focus on the supermatrix model which can be seen as a specific case of two-matrix models. The former has been introduced long time ago and it has been noticed or suggested that its properties might not drastically differ from ordinary one-matrix model, at least in the planar limit. We want here to present how the partition function of the supermatrix model actually differs...

24. Insights from the quantum modularity of 3-manifold invariants

Ioana Coman (Amsterdam)

6/28/22, 11:50 AM

A recently proposed class of topological 3-manifold invariants Zˆ[M] which admit series expansions with integer coefficients has been a focal point of much research over the past few years, proving themselves ubiquitous in a wide range of contexts. They were originally defined physically as an index which computes the BPS spectra of certain supersym- metric quantum field theories in three...

25. From SUSY gauge theories to generalized cohomology to Bethe ansatz

Mykola Dedushenko (SCGP)

6/28/22, 2:00 PM

Supersymmetric ground states and supersymmetric boundary conditions in gauge theories with four supercharges are related to equivariant cohomology theories of their spaces of vacua. When we focus on 3d theories compactified on the elliptic curve, the relevant cohomology theory is elliptic, and upon degenerations to 2d and 1d it reduces to K-theory and de Rham cohomology. Via this connection,...

40. XYZ correlations and Painlevé VI

Hjalmar Rosengren (Chalmers)

6/29/22, 9:30 AM

Baxter solved the XYZ spin chain in the sense of computing the free energy in the infinite lattice limit. For special parameter values, the chain has an underlying supersymmetry. It is then possible to obtain exact results even for finite size systems. In the special case of the XXZ chain, this is related to very interesting combinatorics (e.g. the alternating-sign-matrix and Razumov-Stroganov...

45. Explicit computations for spin chains and the remarkable operator Co-derivative

Helal Aldarak (IMB)

6/29/22, 10:30 AM

In this talk, we are going to show the power of the operator Co-derivative in converting complicated computations into combinatorial relation. To do so, I will consider the twisted spin chain with the underlying Lie algebra gl(n), and show how to obtain the (T,Q) operators using the D-diagrams that arise from using the Co-derivative on the generating series of the characters. Then, we will...

36. Bethe ansatz solution for a new integrable open quantum system

Chiara Paletta (Trinity)

6/29/22, 11:00 AM

In nature, the interaction of a system with the environment cannot be avoided. If the response of the environment is Markovian, the density matrix will evolve through the Lindblad Master equation: dependent on the Hamiltonian of the system and a jump operator describing the coupling to the environment. In PRL 126.24 (2021): 240403, we gave a partial classification of Yang Baxter Integrable...

35. Irrelevant deformations by higher-form symmetries

Bruno Le Floch (Sorbonne)

6/29/22, 11:50 AM

Zamolodchikov and Smirnov discovered how 2d QFTs can be deformed by an antisymmetric combination of two conserved currents. The landmark example is the TTbar deformation constructed from the stress tensor. After explaining which symmetries these deformations preserve, I will explain higher-dimensional generalizations based on higher-form symmetries. This leads to a curious way to couple a...

37. Dendroscopy of BPS states

Boris Pioline (Sorbonne)

6/30/22, 9:30 AM

The spectrum of BPS states in D=4 supersymmetric field theories and string vacua famously jumps across codimension-one walls in vector multiplet moduli space. The Attractor Flow Tree conjecture postulates that the BPS index Ω(γ,z) for given charge γ and moduli z can be reconstructed from the “attractor indices” Ω(γi) counting BPS states of charge γi in their respective attractor chamber, by...

26. Donaldson-Thomas invariants of toric quivers

Pierre Descombes (Sorbonne)

6/30/22, 10:30 AM

A toric localization formula for numerical Donaldson-Thomas invariants, giving the virtual Euler number of moduli spaces which are critical lcus, is known since Graber and Pandharipande. We provide here a refining of this formula for cohomological Donaldson-Thomas invariants, which can be seen as a 'virtual version of Bialinicky Birula decomposition', giving the virtual cohomology of the...

31. Testing 3d IR Dualities Using Algebraic Geometry

Osama Khlaif (Birmingham)

6/30/22, 11:00 AM

In this talk I will revisit some well-studied 3d IR dualities including Aharony Duality and that of Giveon-Kutasov. I will also discuss some recently proposed ones and show how one can connect these dualities together. In the second part, I will show how, using algebraic geometry and supersymmetric localization, one can explicitly compute the twisted supersymmetric index on any Riemann...

41. Equivariant indices and geometry

Maxim Zabzine (Uppsala)

6/30/22, 11:50 AM

33. The Geometry of Magnificent Four

Martijn Kool (Utrecht)

6/30/22, 2:00 PM

Motivated by super-Yang–Mills theory on a Calabi–Yau 4-fold, Nekrasov and Piazzalunga assigned weights to r-tuples of solid partitions (4-dimensional piles of boxes) and conjectured a formula for their weighted generating function. We define K-theoretic virtual invariants of Quot schemes of 0-dimensional quotients of Or on affine 4-space by realizing them as zero loci of isotropic sections of...

34. Branes and DAHA Representations

Peter Koroteev (Berkeley)

7/1/22, 9:30 AM

42. Refined topological strings and qq-characters

Yegor Zenkevich (SISSA)

7/1/22, 10:30 AM

Using the identification of certain topological string amplitudes with R-matrices of Ding-Iohara-Miki algebras we find that qq-charaters can be constructed in a very simple way from degeneration of certain open refined topologcial string amplitudes. We illustrate the construction with several examples.

27. Super-Macdonald polynomials: Orthogonality properties and physical interpretations

Martin Hallnäs (Chalmers)

7/1/22, 11:50 AM

Macdonald polynomials are two-parameter generalizations of Schur polynomials, with important connections to representation theory, geometry as well as integrable systems. In particular, they provide eigenfunctions of Macdonald-Ruijsenaars difference operators, which define an integrable relativistic quantum many-body system. This talk is focused on the so-called super-Macdonald polynomials,...