Large AdS black holes from QFT

TL;DR

The paper studies the N=4 SYM index on S^3×R in generalized Cardy and Macdonald limits to extract the microstate counting of BPS AdS black holes. It employs two complementary QFT approaches (free field analysis and S^3 background-field CS terms) and extends to AdS7 via a background-field treatment on S^5, obtaining leading entropy-like expressions that reproduce known BPS black hole entropies after Legendre transformation. The Macdonald sector suggests small or hairy black-hole saddles beyond the known solutions, signaling richer phase structure in certain BPS sectors. Overall, the work provides a QFT framework for macroscopic black hole entropy in AdS4/5/7 contexts and points to new microstate structures and saddle points with holographic significance.

Abstract

We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$ at large angular momenta. A generalized Cardy limit exhibits macroscopic entropy at large $N$. Our result is derived using free QFT analysis, and also a background field method on $S^3$. The index sets a lower bound on the entropy. It saturates the Bekenstein-Hawking entropy of known supersymmetric AdS$_5$ black holes, thus accounting for their microstates. We further analyze the so-called Macdonald index, exploring small black holes and possibly new black holes reminiscent of hairy black holes. Finally, we study aspects of large supersymmetric AdS$_7$ black holes, using background field method on $S^5$ and 't Hooft anomalies.

Figures (5)

• Figure 1: $\log Z$ as a function of $Q+J$, extrapolating (\ref{['free-energy-final']}) beyond the Cardy limit
• Figure 2: Various solutions $f(r)$ of \ref{['treq']}
• Figure 3: Blue/yellow line denotes the real/imaginary part of (a) $\omega_1$, (b) $\Delta$. Red line denotes $\omega_1, \Delta$ corresponding to $f(r)$ described as the red line in Fig. \ref{['fig: f_r']} (a), which we dismiss.
• Figure 4: $s(q)$ at $j=300$: blue/yellow line denotes its real/imaginary part.
• Figure 5: $|\omega_1|>0.1$ in the region encircled by the red dashed line.