On Three-Dimensional Mirror Symmetry

Abstract

Mirror Symmetry for a large class of three dimensional $\mathcal{N}=4$ supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of $\text{ALE}$ spaces. A pair of such mirror duals can be described as two different deformations of the eleven-dimensional supergravity background $\mathcal{M}={\mathbb{R}}^{2,1}\times {\text{ALE}}_1\times {\text{ALE}}_2$, to which they flow in the deep IR. Using the $A-D-E$ classification of $\text{ALE}$ spaces, we present a neat way to catalogue dual quiver gauge theories that arise in this fashion. In addition to the well-known examples studied in \cite{Intriligator:1996ex}, \cite{deBoer:1996mp}, this procedure leads to new sets of dual theories. For a certain subset of dual theories which arise from the aforementioned M-theory background with an $A$-type ${\text{ALE}}_1$ and a $D$-type ${\text{ALE}}_2$, we verify the duality explicitly by a computation of partition functions of the theories on $S^3$, using localization techniques . We derive the relevant mirror map and discuss its agreement with predictions from the Type IIB brane construction for these theories.

50 pages, 12 figures; comments on the number of FI parameters added

References in corpus (3)

• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Nonperturbative Tests of Three-Dimensional Dualities

Cited by in corpus (13)

• IIB Duals of D=3 N=4 Circular Quivers
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• On Three-Dimensional Quiver Gauge Theories of Type B
• Three Dimensional Mirror Symmetry and Partition Function on $S^3$
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Mirror Symmetry in Three Dimensions via Gauged Linear Quivers
• Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d N=2 supersymmetric theories
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Resolved gravity duals of $\mathcal{N}=4$ quiver field theories in 2+1 dimensions
• Dualities and loops on squashed $S^3$