Two Dimensional Mirror Symmetry From M-theory

TL;DR

This paper constructs 2D N=(4,4) supersymmetric gauge theories from IIA branes, explores their quantum effects via M-theory embedding, and reveals mirror symmetry relating Coulomb and Higgs branches at strong coupling.

Contribution

It introduces a new brane-based construction of 2D supersymmetric gauge theories and analyzes their quantum properties, including mirror symmetry and dualities, within M-theory.

Findings

Coulomb and Higgs branches become equivalent at strong coupling.

Relationship established between IIA/IIB 5-branes and Matrix theory.

T-duality interpreted through brane configurations and string duality puzzles addressed.

Abstract

We construct two dimensional gauge theories with $N= (4,4)$ supersymmetry from branes of type IIA string theory. Quantum effects in the two dimensional gauge theory are analyzed by embedding the IIA brane construction into M-theory. We find that the Coulomb branch of one theory and the Higgs branch of a mirror theory become equivalent at strong coupling. A relationship to the decoupling limit of the type IIA and IIB 5-branes in Matrix theory is shown. T-duality between the ALE metric and the wormhole metric of Callan, Harvey, and Strominger is discussed from a brane perspective and some puzzles regarding string duality resolved. We comment on the existence of a quantum Higgs branch in two dimensional theories. Branes prove to be useful tools in analyzing singular conformal field theories.