Free Energy of D_n Quiver Chern-Simons Theories

TL;DR

This paper computes the free energy of D_n quiver Chern-Simons theories using matrix models, revealing invariance under Seiberg duality and connecting to geometric volumes via AdS/CFT, while exploring quiver relations and flavor effects.

Contribution

It introduces a general, duality-invariant formula for free energy of D_n quivers and relates it to graph theory and geometric volumes, extending understanding of these theories.

Findings

Derived a conjectured free energy formula invariant under Seiberg duality.

Connected free energy to volumes of tri-Sasaki Einstein manifolds via AdS/CFT.

Confirmed that adding massive flavors decreases free energy, supporting the F-theorem.

Abstract

We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of N=3 Chern-Simons matter theories with D_n quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these D_n quivers to A_{2n-5} quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.