Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces

TL;DR

This paper constructs D-brane configurations to realize mirror symmetry in 3D N=4 supersymmetric gauge theories, elucidating the duality via SL(2,Z) symmetry and exploring instanton corrections and transitions in the moduli space.

Contribution

It provides an explicit construction of mirror pairs of 3D gauge theories using D-branes and string dualities, including a general procedure for obtaining mirror theories.

Findings

Explicit D-brane configurations encode dual gauge theories.

Mirror symmetry exchanges Coulomb and Higgs branches.

Instanton corrections are studied via open string instantons.

Abstract

We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N=4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2,Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane worldvolume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping five-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.