Mutations in Quiver Yangians
演讲者
Dmitry Galakhov
时间
2026年04月09日 14:30 至 16:00
地点
A7-302
线上
Zoom 388 528 9728
(BIMSA)
摘要
BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiver variety are interpreted as vectors populating a representation module. The well-known wall-crossing phenomena are that the fixed point spectrum establishes a dependence on the stability (Fayet-Illiopolous) parameters, jumping abruptly across the walls of marginal stability, which divide the space of stability paramters into a collection of chambers -- BPS ``phases'' of the theory. One of constructions of the quiver Yangian algebra relies heavily on the molten crystal model, valid in a sole cyclic chamber where all the stability parameters have the same sign. We propose to lift this restriction and investigate the effects of the wall-crossing phenomena on the quiver Yangian algebra and its representations. We concentrate on two families of examples: affine super Yangian Y(gl(1|1)) and Yangian algebras Y(sl(n)). We describe the BPS spectra outside the cyclic chamber using Seiberg-like dualities (mutations) and their generalizations and investigate effects of mutations on quiver Yangian algebras. The talk is baised on 2403.14600 with A.Morozov and N.Tseousov and on 2601.11736 with A.Gavshin and A.Morozov.