$N^3$-behavior from 5D Yang-Mills theory

TL;DR

The paper investigates $N^3$ scaling in the free energy of 5D maximally supersymmetric YM on $S^5$ by reducing the theory to localization-derived matrix models. It demonstrates $N^3$ scaling at strong coupling for an adjoint hypermultiplet and for a $Z_k$ quiver, with $F \sim -\frac{27}{512}\frac{g_{YM}^2 N^3}{\pi r}$ and $F \sim -\frac{27}{512}\frac{g_{YM}^2 N^3}{\pi k^2 r}$, respectively, while fundamental hypermultiplets yield $F \sim N^2$ for $M\le 2N$ and destabilize otherwise. The results are contrasted with the $AdS_7\times S^4$ gravity dual, revealing a numerical mismatch (e.g., a factor of $81/80$) under standard identifications between $R_6$ and $g_{YM}^2$, and suggesting that the precise $(2,0)$–to–5D YM correspondence or scheme choices may require refinement. The work thus contributes to understanding holography for nonconformal 5D theories and highlights how localization-derived matrix models can test proposed dualities and radius–coupling identifications.

Abstract

In this note we derive $N^3$-behavior at large t' Hooft coupling for the free energy of 5D maximally supersymmetric Yang-Mills theory on $S^5$. We also consider a $Z_k$ quiver of this model, as well as a model with $M$ hypermultiplets in the fundamental representation. We compare the results to the supergravity description and comment on their relation.