Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3

TL;DR

This paper investigates the structure of moduli spaces in 3d N=2 Chern-Simons quiver gauge theories, revealing a connection to 4d theories and providing a method to construct AdS_4/CFT_3 dual pairs with explicit geometric examples.

Contribution

It demonstrates that 3d moduli spaces contain baryonic branches linked to 4d parent theories and offers a systematic approach to find superconformal Chern-Simons theories with gravity duals.

Findings

Moduli spaces include baryonic branches from 4d theories.

Certain Chern-Simons levels produce 4-fold singularities.

Constructed examples of duals to toric Sasaki-Einstein manifolds.

Abstract

We analyse the classical moduli spaces of supersymmetric vacua of 3d 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 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 N=2 superconformal Chern-Simons quivers with AdS_4 gravity duals. As simple, but non-trivial, examples, we identify a family of Chern-Simons quiver gauge theories which are candidate AdS_4/CFT_3 duals to an infinite class of toric Sasaki-Einstein seven-manifolds with explicit metrics.