Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields

TL;DR

This paper extends operator counting methods to analyze N=2 Chern-Simons theories with chiral-like matter, confirming their geometric duals and volume relations in the large-N limit.

Contribution

It applies operator counting techniques to chiral-like models, validating their geometric duals and volume formulas within the AdS/CFT correspondence.

Findings

Operator counting matches volume formulas for chiral-like theories.

Results support the duality between these theories and inhomogeneous Sasaki-Einstein manifolds.

Method extends the applicability of localization and operator counting to chiral models.

Abstract

The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established yet, due to technical problems in both analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested that the counting of chiral operators can be used to find the eigenvalue distribution of quiver matrix models. In this paper we apply this method to some vector-like or chiral-like quiver theories, including the triangular quivers with generic Chern-Simons levels which are dual to in-homogeneous Sasaki-Einstein manifolds $Y^{p,k}(\mathbb{CP}^2)$. The result is consistent with AdS/CFT and the volume formula. We discuss the implication of our analysis.