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# Advances in Theoretical and Mathematical Physics

## Volume 24 (2020)

### Number 2

### A 3d gauge theory/quantum K-theory correspondence

Pages: 327 – 457

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n2.a4

#### Authors

#### Abstract

The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kähler 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 $\mathcal{N} = 2$ 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.

Published 10 July 2020