Moduli spaces of Chern-Simons quiver gauge theories andAdS4/CFT3

Abstract

We analyze the classical moduli spaces of supersymmetric vacua of 3D $\mathcal{N}=2$ Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3D theory always contains a baryonic branch of a parent 4D $\mathcal{N}=1$ quiver gauge theory, where the 4D baryonic branch is determined by the vector of 3D Chern-Simons levels. In particular, starting with a 4D quiver theory dual to a 3-fold singularity, for certain general choices of Chern-Simons levels this branch of the moduli space of the corresponding 3D theory is a 4-fold singularity. Our results lead to a simple general method, using existing 4D techniques, for constructing candidate 3D $\mathcal{N}=2$ superconformal Chern-Simons quivers with ${\mathrm{AdS}}_{4}$ gravity duals. As simple, but nontrivial, examples, we identify a family of Chern-Simons quiver gauge theories which are candidate ${\mathrm{AdS}}_{4}/{\mathrm{CFT}}_{3}$ duals to an infinite class of toric Sasaki-Einstein seven-manifolds with explicit metrics.