From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))

TL;DR

This paper uses matrix models to analyze necklace quiver gauge theories with N=3 supersymmetry, confirming the F-theorem, relating eigenvalues to chiral operators, and deriving the T(U(N)) partition function.

Contribution

It demonstrates the F-theorem for necklace theories, links eigenvalue distributions to operator counts, and computes the T(U(N)) partition function using matrix models.

Findings

F-theorem holds for simple RG flows in necklace theories

Eigenvalue distributions relate to chiral operator counts

Partition function of T(U(N)) on S^3 is derived

Abstract

The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with {\cal N}=3 supersymmetry and U(N)^d gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S^3. The conjectured F-theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S^3.