On the moduli space of elliptic Maxwell-Chern-Simons theories

TL;DR

This paper studies the moduli space of 3D N=3 Maxwell-Chern-Simons theories with brane constructions, revealing their Higgs branch as orbifolds of C^4 and exploring more complex fivebrane configurations.

Contribution

It provides a detailed analysis of the moduli space for these theories, including the case with multiple fivebrane types, and confirms geometric dualities with M-theory.

Findings

Higgs branch is an abelian orbifold of C^4.

Moduli space includes nontoric fourfolds with multiple fivebrane types.

Duality with M-theory geometries is confirmed.

Abstract

We analyze the moduli space of the low-energy limit of 3-dimensional N=3 Maxwell-Chern-Simons theories described by circular quiver diagrams, as for 4-dimensional elliptic models. We define the theories by using D3-NS5-(k,1)5-brane systems with an arbitrary number of fivebranes. The supersymmetry is expected to be enhanced to N=4 in the low-energy limit. We show that the Higgs branch, in which all bifundamental scalar fields develop vacuum expectation values, is an abelian orbifold of C^4. We confirm that the same geometry is obtained as an M-theory dual of the brane system. We also consider theories realized by introducing more than two kinds of fivebranes, and obtain nontoric fourfolds as moduli spaces.