4d mirror symmetry for class-S theories

Geometric Representation

Theory Seminar

Organizers

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker

Wenbin Yan (YMSC)

Time

Wednesday, 15:30 - 16:30

Dec. 11, 2024

Venue

B627, Shuangqing Complex Building A

4d mirror symmetry for class-S theories

I will explain a (conjectural) correspondence between the representation theory of a vertex operator algebra (VOA) associated to a genus g Riemann surface with n-punctures and the geometry of Hitchin moduli space / character variety of the same Riemann surface. They are coming from Higgs / Coulomb branches 0f 4d class-S theories respectively. We propose that there exists a bijection between modular invariant modules of the VOA and fixed manifolds of Hitchin moduli spaces. The modularity is also related to dimensions of fixed manifolds. Moreover, all these data can be read from the mixed Hodge polynomials of the character variety. I will explain this correspondence in detail and provide examples.