Titles and Abstracts

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March 14 (Fri)

Masataka Watanabe  (14:00 -15:00 pm)

Title: 6D moduli effective action and 2D chiral algebra

Abstract: I will use the effective action on the tensor branch moduli space to study large-R-charge operators of 6D SCFTs. This can be thought of as an application of the relatively new method called the large-charge expansion to the notoriously strongly-coupled, non-Lagrangian theories. Concretely, I will compute the OPE coefficients among half-BPS operators at large-R-charge in an asymptotic expansion. I will then use the 6D/2D correspondence of Beem, Rastelli and van Rees to map the OPE to the expansion coefficients of the Virasoro vacuum block in a certain double-scaling limit, at c = 25. I will finally conjecture the behaviour of the Virasoro vacuum block at general central charge in a double-scaling limit that has seldom been studied before. I argue that this could be interpreted as a semi-classicalisation of heavy vacuum descendants.

Naoto Shiraishi   (15:30 -16:30 pm )

Title: Proving non-integrability of some quantum spin systems

Abstract: In this talk, I will explain some recent rigorous results of non-integrability of quantum spin systems in the sense that the system has no local conserved quantity. First, I prove the non-integrability of XYZ chain with z magnetic field in detail, which serves as a prototype of nonintegrability proofs. Then, I present a classification theorem of integrability and non-integrability of all S=1/2 spin chains with symmetric nearest-neighbor interaction.

March 15 (Sat)

Shunsuke Tsuchioka  (10-11 am )

Title: Lepowsky-Wilson Z-algebras and Rogers-Ramanujan type identities

Abstract:  Since Lepowsky-Wilson's vertex operator proof of the Rogers-Ramanujan identities, it has been expected that there exists a Rogers-Ramanujan type identity whose infinite product is given by the principal character of a standard module of an affine Lie algebra. I will report on the cases of A^{(2)}_{2} level 4 (arXiv:1910.12461), A^{(1)}_{2} level 3 (arXiv:2205.04811), D^{(3)}_{4} level 3 and A^{(2)}_{4} level 3  (arXiv:2211.12351).

Tadashi Okazaki   (11:15 -12:15  am )

Title: N=4 Super Yang-Mills theories and decorated supersymmetric indices

Abstract:  The supersymmetric indices can be decorated by various supersymmetric defect operators in such a way that they can enumerate the BPS operators living on the defects. For 4d N=4 supersymmetric gauge theories the action of S-duality on the defects leads to conjectural identities of the indices. Understanding the identities and their generalizations poses challenges in mathematical physics. In particular, in the cases with ABCD-type gauge groups, the configurations with defects can be engineered as brane configurations in Type IIB string theory. They provide an interesting laboratory in which the double holography and the twisted holography can be tested. The indices can encode the spectra of various fluctuation modes on the holographically dual geometries and admit the conjectural expansions, the so-called giant graviton expansions.

Kanehisa Takasaki  (14:00 -15:00 pm )

Title: Logarithmic Lax operator in Toda and lattice KP hierarchies

Abstract: The Lax formalism of the 2D Toda and lattice KP hierarchies is constructed by difference operators on a line.  One can define the logarithm of the Lax operators with the aid of dressing operators.  Those logarithic Lax operators are used to consider exotic reductions of the 2D Toda and lattice KP hierarchies.  I present some of them, in particular, those related to the bigraded Toda hierarchy and the lattice Gelfand-Dickey hierarchy.   

Junya Yagi   (15:30 -16:30  pm )

Title:Quantized six-vertex model on a torus

Abstract: The six-vertex model is arguably the most famous 2D integrable lattice model. Less known is the fact that the model has a 3D origin. In this talk I will discuss the quantization of the six-vertex model, introduced by Kuniba, Matsuike and Yoneyama in 2022 generalizing earlier work of Bazhanov, Mangazeev and Sergeev. The quantized six-vertex model is a 3D integrable lattice model, which has a remarkable property that commuting layer transfer matrices can be defined not only for square lattices but also for more general "admissible" graphs on a torus. Time permitting, I will also explain how the model is related to dimer models, supersymmetric gauge theories and string theory. This is based on joint work with Rei Inoue, Atsuo Kuniba and Yuji Terashima.

March 16 (Sun)

Toshiaki Shoji (10-11 am )

Title: Algorithm of computing canonical bases, and foldings of  quantum groups 

Abstract:  Let U^- be the negative half of the quantum group of finite type. U^- has good bases, called "canonical bases" and "PBW bases". Canonical bases are important for the representation theory of quantum groups. The computation of PBW bases is easy, but the direct computation  of canonical bases is difficult.  Hence it is important to compute  the transition matrix P  between canonical bases and PBW bases.  In U^-, there exist another type of bases, called "monomial bases".

By using the monomial bases, we can give a simple algorithm of computing  P,  which is an algorithm of computing canonical bases. 

By the folding theory of quantum groups, the quantum group U_1^-  of symmetric type, with an automorphism, is closely related to  the quantum group U_2^- of non-symmetric type, such as U_1^- of  type A_{2n-1} and U_2^- of type B_n. In this talk, we compare the algorithm of computing canonical basis  for U_1^- and U_2^-, and show that the matrix P_2 for U_2^- can be  determined completely form the information for monomial bases of U_1^-   (but P_2 can not be obtained from the matrix P_1 for U_1^-).

Kazumi  Okuyama (11:15- 12:15am )

Title: Recent developments in double-scaled SYK

Abstract: SYK model is an interesting toy model of holographic duality. In particular, the so-called double-scaled SYK (DSSYK), which is defined by taking a large N limit with the number p of the p-body interaction scaled as p=N^(1/2),  has attracted a lot of attention recently since DSSYK is exactly solvable thanks to the underlying quantum group symmetry. In this talk, I will briefly review the recent developments in DSSYK.