Titles, Abstracts and Slides

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January 12 (Sat)

Antonio Sciarappa (KIAS) [slide (PDF, 1MB)]

Title: Supersymmetric gauge theories and elliptic quantum integrable systems

Abstract:

In this talk we will discuss the relation between 4d, 5d supersymmetric gauge theories and quantum integrable systems with elliptic potential (such as Calogero-Moser and Ruijsenaars-Schneider). As we will see, an exact analytic solution to such integrable systems can be constructed from VEVs of gauge theory observables; sometimes however these need to be corrected by appropriate terms, non-perturbative in the Planck constant (or Omega background parameter), which can be completely determined from the properties of the integrable system.

Toshio Nakatsu (Setsunan University) [slide (PDF, 307KB)]

Title: Three-partition Hodge integrals and the topological vertex

Abstract:

An equivalence between the generating functions of three-partition Hodge inte- grals and the topological vertex is shown. The proof is based on extended shift symmetries of a quantum torus algebra that appear in the fermionic representation of the generat- ing functions. Moreover, these lead to an unexpected relation with the generalized KdV hierarchy. This is a joint work with Kanehisa Takasaki.

References

[1] J. Li, C-C. M. Liu, K. Liu and J. Zhou, A mathematical theory of the topological vertex, Geom. Topol. 13 (2009), 527-621.

[2] M. Aganagic, A. Klemm, M. Marino and C. Vafa, The topological vertex, Commun. Math. Phys. 254 (2005), 425-478.

[3] T. Nakatsu and K. Takasakai, Three-partition Hodge integrals and the topological vertex, to appear.

Yutaka Yoshida (Kavli IPMU) [slide (PDF, 3MB)]

Title: Equivariant U(n) Verlinde algebra from Bethe/Gauge correspondence

Abstract:

Various 4d/2d dualities are obtained by compactification of six dimensional (2,0) theory by Riemann surface. When we focus on the Coulomb branch limit of the lens space superconformal index in 4d side, the relevant two dimensional topological field theory on Riemann surface is believed to be topologically twisted Chern-Simons-matter theory with an adjoint chiral multiplet with R-charge r = 2 on the direct product of circle and Riemann surface. We compute topologically twisted indices of U(n) and SU(n) Chern-Simons-matter theories in terms of supersymmetric localization and quantum integrability. By using supersymmetric localization technique, the path integral of Chern-Simons-matter theory localizes to the Bethe equation of q-boson model which allows us to represent an algebra of Wilson loops as one parameter deformation of Verlinde algebra (equivariant Verlinde algebra) by C. Korff. We confirm the proposed duality to the Coulomb branch limit of the lens space superconformal index for SU(2) and SU(3) with lower levels.

This talk is based on a joint work with Hiroaki Kanno and Katsuyuki Sugiyama.

Takeshi Ikeda (Okayama University of Science)

Title:  Relativistic Toda lattice and K-theoretic Peterson isomorphism

Abstract:

I will explain how a special solution of the relativistic Toda lattice provides a non-trivial relation between the quantum K-theory of the flag variety and the K-homology of the affine Grassmannian. By the connection, we have a dictionary from quantum K-Schubert calculus into affine K-Schubert calculus. I would like to discuss some outcome of it in more details. The talk is based on a joint work with S. Iwao and T. Maeno.

January 13 (Sun)

Atsuo Kuniba (University of Tokyo) [slide (PDF, 2.2MB)]

Title: Aspects of reflection equations

Abstract:

I survey recent progress on reflection equation and its generalization. The topic encompasses 3D approach connected to the quantized coordinate ring, coideal subalgebra of quantum affine algebras and matrix product constructions, etc. 

Kentaroh Yoshida (Kyoto University) [slide (PDF, 2MB)]

Title: Yang-Baxter deformations and generalized supergravity

Abstract:

Recently, there has been a fundamental and significant development in the Green-Schwarz (GS) formulation of superstring theory. In this formulation, the kappa- symmetry plays a central role to ensure the consistency of the theory. In 2016, Tseytlin and Wulff showed that the kappa-symmetry constraints of the GS superstring defined on an arbitrary background lead to a “generalized” supergravity, which contains an additional (non-dynamical) vector field, rather than the standard supergravity. This result indicates that we might have overlooked a potentially important ingredient in the low- energy effective theory of string theory for long time, and may open up new directions including phenomenology and cosmology.

In this talk, I will give an overview on the progress on Yang-Baxter deformations of the AdS5 × S5 superstring and the generalized supergravity. Finally, I would like to discuss Weyl invariance of string theories on generalized supergravity backgrounds.

Masaki Shigmeori (Nagoya University) [slide (PDF, 1.7MB)]

Title: Supercharging Superstrata

Abstract:

Superstrata are the most general microstate geometries known so far for the 3-charge D1-D5-P black hole with known CFT duals, and have attracted much recent attention as a useful playground for studying the microstate structure of black holes. In this talk, I present a new branch of superstrata which is much simpler than the original superstrata. The original superstrata were constructed using a solution-generating tech- nique using bosonic generators of the super-isometry group SU(1,1|2)2 of AdS3 ×S3. The new superstrata are constructed using fermionic generators of SU(1,1|2)2.

Tomohiro Sasamoto (Tokyo Institute of Technology) [slide (PDF, 1.6MB)]

Title:  KPZ fluctuations for a two species asymmetric exclusion process

Abstract:

Since the work by Johansson in 2000 for the totally asymmetric simple exclusion process (TASEP), many works have shown that the limiting current fluctuations of various stochastic interacting particle systems are given by the Tracy-Widom (TW) type distributions, widening the applicability of the Kardar-Parisi-Zhang (KPZ) universality class. However, the results so far have been restricted to single component models.

In this presentation we report on our recent study of a two-species asymmetric exclusion process, known as the Arndt-Heinzel-Rittenberg (AHR) model, in which two species of particles stochastically hop in the opposite directions and swap their positions when they meet [1]. We first apply the Bethe ansatz and construct the transition probability. From this we obtain a multiple integral formula for a certain current fluctuation and show that in the scaling limit it tends to the product of a GUE TW and a Gaussian. Our work is also considered as the first microscopic confirmation of the nonlinear fluctuating hydrodynamics proposed by H. van Beijeren [2] and H. Spohn [3].

This is based on a joint work with Z. Chen, J. de Gier and I. Hiki [4].

References

[1] P. F. Arndt, T. Heinzel, V. Rittenberg, J. Stat. Phys. 97, 1 (1999).

[2] H. van Beijeren, Phys. Rev. Lett. 108, 180601 (2012).

[3] H. Spohn, J. Stat. Phys. 154, 1191 (2014).

[4] Z. Chen, J. de Gier, I. Hiki, and T. Sasamoto, Phys. Rev. Lett. 120, 240601 (2018).