Calabi-Yau Mirror Symmetry as a Gauge Theory Duality

TL;DR

This paper explores two dualities in 2D N=(2,2) supersymmetric gauge theories, demonstrating how they relate Calabi-Yau sigma models through mirror symmetry and T-duality, leading to geometric mirror symmetry.

Contribution

It introduces a novel duality specific to two dimensions that, combined with 3D mirror symmetry, explains Calabi-Yau mirror symmetry via gauge theory dualities.

Findings

Dualities relate Higgs and Coulomb branches of gauge theories.

T-duality maps Calabi-Yau target spaces with torsion.

Sequential dualities produce geometric mirror symmetry.

Abstract

We show that there are two different dualities of two dimensional gauge theories with N=(2,2) supersymmetry. One is basically a consequence of 3d mirror symmetry. The non-linear sigma model with Calabi-Yau target space on the Higgs branch of the gauge theory is mapped into an equivalent non-linear sigma model on the Coulomb branch of the dual theory, realizing a T-dual target space with torsion. The second duality is genuine to two dimensions. In addition to swapping Higgs and Coulomb branch it trades twisted for untwisted multiplets, implying a sign flip of the left moving U(1)_R charge. Succesive application of both dualities leads to geometric mirror symmetry for the target space Calabi-Yau.