A 3d Gauge Theory/Quantum K-Theory Correspondence

TL;DR

This paper extends the 2d gauged linear sigma model/quantum cohomology correspondence to a 3d setting, connecting 3d gauge theories with quantum K-theory and exploring new phenomena like BPS invariants and mirror symmetry.

Contribution

It introduces a 3d gauge theory framework that deforms the 2d correspondence, revealing novel features in BPS invariants, chiral rings, and mirror symmetry.

Findings

Establishes a 3d gauge theory/quantum K-theory correspondence.

Identifies a one-parameter deformation of the 2d model.

Explores new properties like BPS invariants and mirror symmetry in 3d.

Abstract

The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kahler manifold X, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence, where the UV model is the N=2 supersymmetric 3d gauge theory and the IR limit is given by Givental's permutation equivariant quantum K-theory on X. This gives a one-parameter deformation of the 2d GLSM/quantum cohomology correspondence and recovers it in a small radius limit. We study some novelties of the 3d case regarding integral BPS invariants, chiral rings, deformation spaces and mirror symmetry.