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

TL;DR

The paper addresses constructing AdS$_4$/CFT$_3$ duals from 3d ${\cal N}=2$ Chern-Simons quivers by analyzing their classical vacuum moduli spaces. It shows a baryonic branch inherited from a parent 4d ${\cal N}=1$ quiver, controlled by the CS level vector, which can become a Calabi–Yau 4-fold for CS levels with $\sum_i k_i=0$; this provides a practical method to generate candidate conformal CS quivers from known 4d toric quivers. The work develops a unified framework for both Abelian and non-Abelian quivers, including a refined quotient description $\mathscr{M}_{\mathrm{3d}}(k)=\mathcal{Z}//H_k^{\mathbb{C}}$ and the role of the kernel of the CS-character, and it connects to the ABJM construction as a motivating special case. Explicitly, the authors construct a family of CS quivers whose moduli spaces realize cones over toric Sasaki–Einstein seven-manifolds, notably matching the geometry of $Y^{p,k}(\mathbb{C}P^2)$, thus illustrating the method and its potential for broad AdS$_4$/CFT$_3$ applications.

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.

Figures (1)

• Figure 1: Quiver diagram for the candidate CS gauge theory duals of $Y^{p,k}(\mathbb{C} P^2)$.