Exact results for five-dimensional superconformal field theories with gravity duals

TL;DR

This paper uses supersymmetric localization to exactly compute the $S^5$ partition function of five-dimensional superconformal field theories with gravity duals, confirming the $N^{5/2}$ scaling predicted by supergravity.

Contribution

It provides the first exact localization-based computation of the $S^5$ free energy for these theories, matching holographic predictions.

Findings

Exact $S^5$ partition functions computed for 5D SCFTs.

Confirmed the $N^{5/2}$ scaling of free energy.

Found perfect agreement with holographic entanglement entropy calculations.

Abstract

We apply the technique of supersymmetric localization to exactly compute the $S^5$ partition function of several large $N$ superconformal field theories in five dimensions that have $AdS_6$ duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the $S^5$ free energy to a holographic computation of entanglement entropy in the $AdS_6$ duals and find perfect agreement. In particular, we reproduce the $N^{5/2}$ scaling of the $S^5$ free energy that was expected from supergravity.