Moduli Space of Vacua of Supersymmetric Chern-Simons Theories and Type IIB Branes

TL;DR

This paper explores the relationship between the moduli space of vacua in 3D supersymmetric Chern-Simons theories and brane configurations, revealing new phases and stringy vortex states.

Contribution

It establishes a detailed correspondence between vacua moduli spaces and brane setups, including novel symmetric and asymmetric phases in Chern-Simons theories.

Findings

Number of massless scalars matches D3-brane directions.

Identification of symmetric and asymmetric phases.

Stringy vortex states in the asymmetric phase.

Abstract

We study the correspondence between the moduli space of vacua of three-dimensional supersymmetric Yang-Mills (Maxwell) Chern-Simons theories and brane configurations with (p,q)5-brane. For Coulomb branches, the number of the massless adjoint scalar fields in various supersymmetric theories exactly coincides with the number of the freely moving directions of D3-branes stretched between two 5-branes. When we include a matter superfield into the supersymmetric Chern-Simons theory two distinct symmetric and asymmetric phase appear. The symmetric phase is peculiar to this Chern-Simons Higgs system. We find the corresponding brane configuration for these phases. We also identify the stringy counterpart of the topological vortex state in the asymmetric phase.