Mirror symmetry for N=1 QED in three dimensions
Martin Gremm, Emanuel Katz
TL;DR
This work constructs a three-dimensional ${\cal N}=1$ QED theory with $N_f$ flavors using Type IIB branes and proposes an infrared dual via S-duality, where the Higgs branch of the original theory maps to the Coulomb branch of the mirror. Parity invariance is invoked to argue that neither branch can be lifted by quantum corrections, suggesting a robust IR equivalence despite the lack of holomorphy in ${\cal N}=1$ theories. The mirror is described as a $U(1)^{N_f-1}$ theory with ${\cal N}=4$ hypermultiplets, with mass parameters in the original theory corresponding to FI parameters in the mirror, and the Coulomb branch is shown to have the same real dimension as the Higgs branch of the original theory. Verification of the duality is constrained by the absence of holomorphic protection and by quantum corrections to moduli-space metrics, though the brane construction provides consistent mapping and motivates extending mirror symmetry concepts to ${\cal N}=1$ theories; non-Abelian cases remain challenging but potentially tractable within this brane framework.
Abstract
We construct three-dimensional N=1 QED with N_f flavors using branes of type IIB string theory. This theory has a mirror, which can be realized using the S-dual brane configuration. As in examples with more supersymmetry, the Higgs branch of the original theory gets mapped into the Coulomb branch of the mirror. We use parity invariance to argue that these branches cannot be lifted by quantum corrections.