Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling

TL;DR

This paper numerically analyzes the free energy of a specific Chern-Simons-matter theory, revealing subleading logarithmic corrections to the dominant $N^{5/3}$ scaling, and suggests potential universality of these corrections.

Contribution

It provides the first numerical evidence for subleading logarithmic corrections in theories with $N^{5/3}$ scaling and conjectures their universality.

Findings

Identified a $(2/9)\log N$ correction to the free energy.

Discovered a $-(1/18)\log k$ correction.

Proposed the universality of the $rac{2}{9}\log N$ term in similar theories.

Abstract

We numerically investigate the sphere partition function of a Chern-Simons-matter theory with $SU(N)$ gauge group at level $k$ coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order $N^{5/3}$ behavior of the free energy, we find numerical evidence for a term of the form $(2/9)\log N-(1/18)\log k$. We conjecture that the $(2/9)\log N$ term may be universal in theories with $N^{5/3}$ scaling in the large-$N$ limit with the Chern-Simons level $k$ held fixed.