Quantum sheaf cohomology on Grassmannians

TL;DR

This paper explores the quantum sheaf cohomology of Grassmannians with tangent bundle deformations, extending previous abelian results to nonabelian GLSMs using localization and effective potential methods.

Contribution

It introduces a new approach to compute quantum sheaf cohomology for nonabelian GLSMs, combining physics techniques with classical results.

Findings

Derived quantum ring structure from one-loop effective potential

Computed A/2 correlation functions using supersymmetric localization

Validated results through explicit examples

Abstract

In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.