Title: Weyl covariance of M2-brane matrix models and Painlevé equations

Speaker: Dr. Tomoki Nosaka

Affiliation: Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences （中国科学院大学卡弗里理论科学研究所）

Time: 16:00-17:00, Tuesday, 27th June, 2023 (UTC+8, Beijing Time)

Venue: Room 1502, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing

   （东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）

Inviter: Tadashi Okazaki

Abstract  

A large class of the theories of M2-branes can be constructed by the type IIB brane setups of Hanany-Witten type. The partition function of these theories enjoy discrete symmetries, part of which can be understood as the IR dualities associated with the Hanany-Witten transitions. The symmetries become manifest under the equivalence between the partition functions and the quantization problem of one-dimensional curves (Fermi gas formalism), where the symmetries are the coordinate transformations of the associated curves. In particular, when the symmetry is an exceptional Weyl group, it suggests that the partition function solves a non-linear integrable system called q-discrete Painlevé equation associated with the Weyl group. We demonstrate this explicitly for the case where the symmetry is E5 (= SO(10)) Weyl group, finding novel identities among the partition functions at different ranks of the gauge groups and other parameters.

Speaker

Dr. Tomoki Nosaka is currently a postdoctoral fellow of theoretical physics at Kavli Institute for Theoretical Sciences (KITS), University of Chinese Academy of Sciences in Beijing. He received his B.S. in physics in 2011, and Ph.D in physics in 2016, from Kyoto University, Japan. After graduation he worked as a postdoctoral fellow in Korea Institute for Advanced Study in Korea, SISSA in Italy, RIKEN in Japan. He moved to the current position at KITS from April 2022. His main research interests are string theory, M-theory, supersymmetric gauge theories and non-perturbative calculations in these theories, with the motivations to understand quantum gravity as well as to find new mathematical structures behind these objects.