Evidence for a 5d F-theorem

TL;DR

This paper provides evidence for a 5d F-theorem by analyzing RG flows between 5d SCFTs using supergravity duals, deriving a general free energy expression, and showing monotonic behavior along flows.

Contribution

It introduces a new supergravity-based method to compute the free energy on S^5 for 5d SCFTs and demonstrates the monotonicity of free energy in RG flows, supporting the 5d F-theorem.

Findings

Free energy on S^5 expressed via trilogarithm functions.

Solutions extremize a trial free energy based on regularity conditions.

Free energy decreases monotonically along RG flows, confirming the 5d F-theorem.

Abstract

Renormalization group flows are studied between 5d SCFTs engineered by $(p,q)$ 5-brane webs with large numbers of external 5-branes. A general expression for the free energy on $S^5$ in terms of single-valued trilogarithm functions is derived from their supergravity duals, which are characterized by the 5-brane charges and additional geometric parameters. The additional geometric parameters are fixed by regularity conditions, and we show that the solutions to the regularity conditions extremize a trial free energy. These results are used to survey a large sample of $\mathcal O(10^5)$ renormalization group flows between different 5d SCFTs, including Higgs branch flows and flows that preserve the $SU(2)$ $R$-symmetry. In all cases the free energy changes monotonically towards the infrared, in line with a 5d $F$-theorem.