Entropy of near-extremal black holes in AdS_5

TL;DR

This work analyzes near-extremal black holes in $AdS_5 \times S^5$, proposing that their microstates are a dilute gas of defects on heavy BPS operators in ${\cal N}=4$ SYM, i.e., open strings on giant gravitons. The authors develop decoupling limits that isolate light degrees of freedom, revealing IR dualities that exchange the gauge-group rank $N$ with the number of giant gravitons and producing AdS$_3$ and AdS$_2$ sectors in the two- and three-charge cases, respectively; the two-charge sector yields a 2D CFT whose central charge matches the spacetime entropy, while the three-charge sector points to an SCQM on triple intersections. They perform both a zero-coupling partition-function analysis and a combinatorial defect-counting approach, finding $N$-scaling consistent with the gravitational entropy in relevant regimes and highlighting a near-phase-transition structure reminiscent of the Horowitz-Polchinski correspondence. Naked timelike singularities in the two-charge system near critical non-extremality are identified, with a string-theoretic expectation of resolution via new IR geometries or microstate constructions. Overall, the paper supports a microscopic, brane-intersection/open-string picture for near-extremal AdS$_5$ black hole entropy and uncovers a rich web of IR dualities and lower-dimensional AdS/CFT correspondences arising from the giant-graviton sector.

Abstract

We construct the microstates of near-extremal black holes in AdS_5 x S^5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S^5, and we show that they dominate the entropy by directly enumerating them and comparing the results with a partition sum calculation. We display new decoupling limits in which the field theory of the lightest open strings on the D-branes becomes dual to a near-horizon region of the black hole geometry. In the single-charge black hole we find evidence for an infrared duality between SU(N) Yang-Mills theories that exchanges the rank of the gauge group with an R-charge. In the two-charge case (where pairs of branes intersect on a line), the decoupled geometry includes an AdS_3 factor with a two-dimensional CFT dual. The degeneracy in this CFT accounts for the black hole entropy. In the three-charge case (where triples of branes intersect at a point), the decoupled geometry contains an AdS_2 factor. Below a certain critical mass, the two-charge system displays solutions with naked timelike singularities even though they do not violate a BPS bound. We suggest a string theoretic resolution of these singularities.