Verlinde/Grassmannian Correspondence and Rank 2 $\delta$-wall-crossing

Abstract

Motivated by Witten's work (arXiv:hep-th/9312104), we propose the Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian. We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated to the Grassmannian. We construct two families of stability conditions connecting the two theories and prove two wall-crossing results. We confirm the Verlinde/Grassmannian correspondence in the rank two case.

v2: Added Section 6 on K-theoretic quasimap invariants with level structure and the $\delta =\infty$ to $\epsilon =0+$ wall-crossing; typos fixed; some references added