A correspondence between the quantum K theory and quantum cohomology of Grassmannians

TL;DR

This paper explores the deep connections between quantum K theory and quantum cohomology of Grassmannians, using physics-inspired methods and mathematical conjectures to relate different quantum invariants.

Contribution

It establishes a novel correspondence between quantum K theory and quantum cohomology rings of Grassmannians, incorporating physics arguments and the nonabelian/abelian correspondence.

Findings

Relates quantum K theory to twisted quantum cohomology

Connects quantum K pairing with supersymmetric localization correlators

Provides mathematical conjectures with illustrative examples

Abstract

We utilize physics arguments, and the nonabelian/abelian correspondence, to relate the Givental and Lee's quantum K theory ring of Grassmannians to a twisted variant of the quantum cohomology ring. Furthermore, the quantum K pairing is related to correlators arising from supersymmetric localization. We state some mathematical conjectures, which we illustrate in several examples.