Yaoxiong Wen: 3d Toric Mirror Symmetry

Abstract: In this talk, I will introduce a new version of 3d mirror symmetry for toric stacks, inspired by a 3d N=2 abelian mirror symmetry construction in physics introduced by Dorey-Tong. More precisely, for a short exact sequence

                           0 -> Z^k -> Z^n -> Z^{n-k} -> 0,

we consider the toric Artin stack $[C^n/(C^*)^k]$, and its mirror is given by the Gale dual of the above exact sequence, i.e., $[C^n/(C^*)^{n-k}]$. 

We introduce the modified equivariant K-theoretic I-functions for the mirror pair; they are defined by the contribution of fixed points. Under the mirror map, which switches the Kälher parameters and equivariant parameters and maps $q$ to $q^{-1}$, we see that modified I-functions with the effective level structure of mirror pair coincide. This talk is based on the joint work with Yongbin Ruan and Zijun Zhou.