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

Yongbin Ruan; Ming Zhang

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

Algebraic Geometry 2019-07-23 v2

Authors: Yongbin Ruan , Ming Zhang

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.

Keywords

verlinde numbers grassmannian quasimap invariants gauged linear sigma model wall-crossing k-theory stability conditions

Cite

@article{arxiv.1811.01377,
  title  = {Verlinde/Grassmannian Correspondence and Rank 2 $\delta$-wall-crossing},
  author = {Yongbin Ruan and Ming Zhang},
  journal= {arXiv preprint arXiv:1811.01377},
  year   = {2019}
}

Comments

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

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

Abstract

Keywords

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