Large AdS$_6$ black holes from CFT$_5$

TL;DR

This work develops a Cardy-limit analysis of the index for 5d SCFTs on $S^4\times \mathbb{R}$ in the large $N$ regime, focusing on theories engineered from D4-D8-O8 systems. By complexifying holonomies and exploiting a large-$N$ saddle with width $\sim N^{1/2}$, the authors show the perturbative, instanton-suppressed free energy scales as $\log Z\sim N^{5/2}$ and matches the entropy of large BPS AdS$_6$ black holes, establishing a precise field-theory accounting for black hole microstates. They compute explicit Cardy free energies for $Sp(N)$ and $SU(2N)$ quivers with constrained chemical potentials, and derive the corresponding entropy function via a Legendre transform, reproducing the universal AdS$_6$ BH entropy when baryonic and mesonic charges vanish. The analysis clarifies the subtle role of instantons in 5d deconfinement, arguing that $Z_{\rm inst}$ is effectively unity at the dominant large-$N$ saddle, while also highlighting the potential for richer saddle structures beyond the Cardy limit. The results support a holographic picture of 5d deconfinement and offer a framework to explore broader 5d SCFTs and their AdS$_6$ duals.

Abstract

We study supersymmetric AdS$_6$ black holes at large angular momenta, from the index of 5d SCFTs on $S^4\times\mathbb{R}$ in the large $N$ and Cardy limit. Our examples are the strong coupling limits of 5d gauge theories on the D4-D8-O8 system. The large $N$ free energy scales like $N^{5/2}$, statistically accounting for the entropy of large black holes in AdS$_6$. Instanton solitons play subtle roles to realize these deconfined degrees of freedom.