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

Abstract

We investigate the $S^3$ free energy of $\mathcal{N}=3$ Chern-Simons-matter quiver gauge theories with gauge group $U(N{)}^r(r\ge 2)$ 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.

v1: 50 pages, 1figure; v2: minor revisions

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Cited by in corpus (1)

• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization