M-Theory Origin of Mirror Symmetry in Three Dimensional Gauge Theories

TL;DR

The paper embeds a known three-dimensional ${\\cal N}=4$ gauge-theory duality into M-theory by examining compactifications on $K_3\times K_3$ with membranes near $A_n$ or $D_n$ singularities. By recasting the same M-theory configuration in two equivalent Type I' descriptions—each leading to a different 3D world-volume gauge theory—the authors show that the intrinsic mirror symmetry exchanges the Coulomb and Higgs branches and swaps masses with Fayet–Iliopoulos terms, providing a geometric origin for the duality. The Kronheimer construction of ALE spaces and its gauge-theory realization via D-branes are used to connect the hyper-Kähler quotient moduli spaces to the probe dynamics, enabling a unified quiver-based framework that reproduces Intriligator–Seiberg dual pairs and yields new dual pairs. The approach generalizes to multiple ALE pairs and quiver diagrams, offering a brane-based derivation of a broad class of 3D ${\\cal N}=4$ dualities with concrete predictions for moduli-space dimensions and parameter counts. This work thus links M-theory, ALE/K3 geometry, and quiver gauge theories to give a concrete, two-fold realization of three-dimensional mirror symmetry with new dual candidates.

Abstract

We present M-theory compactifications on $K_3 \times K_3$ with membranes near the $A_n$ or $D_n$ singularities of the $K_3$ spaces. By realizing each of these compactifications in two different ways as type I' models with 2- and 6-branes, we explain the three-dimensional duality between gauge theories recently found by Intriligator and Seiberg. We also find new pairs of dual gauge theories, which we briefly describe.