Mirror Symmetry and Bosonization in 2d and 3d

TL;DR

This paper explores how mirror symmetry in 2d supersymmetric theories and 3d dualities flow to bosonization in the infrared, providing exact maps and extending to non-supersymmetric cases.

Contribution

It demonstrates the flow from mirror symmetry to bosonization in 2d and extends the analysis to 3d dualities compactified on a circle, deriving exact bosonization maps.

Findings

Mirror symmetry flows to 2d bosonization in the IR.

Exact bosonization map derived at one-loop.

3d dualities reduce to 2d bosonization upon circle compactification.

Abstract

We study a supersymmetry breaking deformation of the 2d N=(2,2) cigar=Liouville mirror pair, first introduced by Hori and Kapustin. We show that mirror symmetry flows in the infra-red to 2d bosonization, with the theories reducing to massive Thirring and Sine-Gordon respectively. The exact bosonization map emerges at one-loop. We further compactify non-supersymmetric 3d bosonization dualities on a circle and argue that these too flow to 2d bosonization at long distances.