Chern-Simons-Matter Theory and Mirror Symmetry

TL;DR

The paper analyzes abelian and nonabelian Chern-Simons-matter theories in 2+1 dimensions, focusing on cases with multiple Higgs branches meeting at a quantum critical point. It demonstrates that certain ${\cal N}=4$ CSM theories realize the IR SCFT of ${\cal N}=4$ QED with $N_f$ flavors, with the mirror symmetry exchanging Coulomb and Higgs branches becoming explicit in the Lagrangian; brane constructions and symmetry enhancements provide nontrivial checks for $N_f=2$ and $N_f=3$. The authors show that hypermultiplet moduli spaces in CS theories can receive quantum corrections, computable via one-loop analysis, yielding corrected hyperkähler quotients that match the IR fixed-point geometries. They also extend the discussion to ${\cal N}=2$ CS-matter theories, where moduli spaces can be lifted or restored depending on the CS levels, and present both abelian and simple nonabelian generalizations, laying groundwork for broader connections to SQCD-like IR SCFTs and potential gravity duals.

Abstract

In this paper we study supersymmetric Chern-Simons-matter (CSM) theories with several Higgs branches. Two such theories at small Chern-Simons level are conjectured to describe the superconformal field theory at the infrared fixed point of N = 4 QED with N_f = 2, 3. In particular, the mirror symmetry which exchanges the Coulomb and Higgs branches of N = 4 QED with N_f = 2 is manifest in the Chern-Simons-matter description. We also study the quantum corrections to the moduli space of a class of N = 2 CSM theories.