Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 2

A 3d gauge theory/quantum K-theory correspondence

Pages: 327 – 457



Hans Jockers (Bethe Center for Theoretical Physics, Physikalisches Institut, Universität Bonn, Germany)

Peter Mayr (Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Munich, Germany)


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