Mirror Symmetry in Three Dimensional Gauge Theories

TL;DR

This paper explores a new mirror symmetry duality in three-dimensional N=4 gauge theories, exchanging Higgs and Coulomb branches, with implications for understanding instanton moduli spaces and string theory phenomena.

Contribution

It introduces a novel duality acting as mirror symmetry in 3D N=4 gauge theories, relating Higgs and Coulomb branches and providing new insights into instanton moduli spaces and string theory.

Findings

Dual theories have Higgs and Coulomb branches as ALE spaces.

Coulomb branches are related to instanton moduli spaces.

Small E8 instantons are described by local quantum field theories.

Abstract

We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $ADE$ gauge group. In particular, we show that in three dimensions small $E_8$ instantons in string theory are described by a local quantum field theory.