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

TL;DR

The paper analyzes the Higgs branch of 3D ${\cal N}=3$ Maxwell-Chern-Simons theories realized by circular quivers engineered with D3-NS5-(k,1)5-brane systems. In the infrared, the theory is expected to flow to ${\cal N}=4$ and the Higgs branch is shown to be an abelian orbifold ${\mathbb C}^4/\Gamma$ with $|\Gamma|=kn_A n_B$, consistent with an M-theory dual. Extending the construction to more than two brane types yields a 4-dimensional moduli space that can be non-toric, illustrating rich geometric structures beyond toric Calabi-Yau cases. The results illuminate the brane-geometry dictionary for 3D quiver CS theories and provide a concrete setting to explore AdS/CFT in novel M-theory backgrounds.

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.

Figures (4)

• Figure 1: Brane configuration for the $U(N)\times U(N)$ Chern-Simons model.
• Figure 2: Brane system and fields.
• Figure 3: Toric diagram of a generalized conifold.
• Figure 4: (a) M-theory dual of the D3-fivebrane system in $36r_3$ space. This can be regarded as a webdiagram of the toric geometry. The corresponding toric diagram is shown in (b).