Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA

TL;DR

This paper analyzes the sub-leading corrections to the $S^3$ free energy in certain $ ext{AdS}_4/ ext{CFT}_3$ dual pairs, using matrix models and Fermi-gas methods to uncover universal logarithmic corrections.

Contribution

It provides the first detailed computation of sub-leading $1/N$ corrections to the free energy of necklace quiver theories with non-vanishing Chern-Simons levels, using two complementary approaches.

Findings

Consistent results between saddle point and Fermi-gas methods at sub-leading order.

Identification of a universal $rac{1}{6} ext{log}N$ correction to the free energy.

Insights into holographic dual corrections in massive Type IIA theories.

Abstract

We investigate the $S^3$ free energy of $\mathcal N=3$ Chern-Simons-matter quiver gauge theories with gauge group $U(N)^r~(r\geq2)$ where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-$N$ expansion. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the 't~Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy $F=-\log Z$ are consistent with each other at the leading and first sub-leading order. The Fermi-gas approach also hints at a universal $\frac{1}{6}\log N$ correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect our results to match sub-leading corrections to the holographic dual free energy, which have not yet been fully investigated.