Supersymmetric Defect Models and Mirror Symmetry

TL;DR

This paper explores supersymmetric defect configurations in 3d field theories, demonstrating how mirror symmetry relates electric and magnetic defects, and analyzing their implications for impurity models and ground state entropy.

Contribution

It introduces supersymmetric impurity models in 3d theories, showing how mirror symmetry relates electric and magnetic defects and providing solutions for defect arrays in N=4 QED.

Findings

Mirror symmetry relates electric and magnetic defect configurations.

Backreacted solutions for defect arrays in N=4 QED are obtained.

Insights into particle-vortex duality and ground state entropy at finite density.

Abstract

We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d N=4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d N=2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of N=4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.