One-Loop Test of Quantum Black Holes in anti–de Sitter Space

Abstract

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS_{4} black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

Microstate counting via Bethe Ansätze in the 4d $$ \mathcal{N} $$ = 1 superconformal index

“…For example, the statistical entropy of certain magnetically charged AdS 4 black holes has recently been given a microscopic explanation in terms of the topologically twisted index [1] (see [2,3] for a reviews with comprehensive lists of references). The investigation of sub-leading (logarithmic in N) corrections such as those performed recently [35,36] have helped clarify the nature of the degrees of freedom on the gravitational side of the duality. One would hope for similar developments in the context of AdS 5 black holes.…”

One-loop determinants for black holes in 4d gauged supergravity

“…Logarithmic corrections to the Bekenstein-Hawking entropy of certain asymptotically AdS 4 solutions have been computed, both in 11d supergravity using zero-mode counting [17,18] and in the dual field theory at the level of the topologically twisted index [16,23,24,26]. Comparison with previous results for specific models would first require us to fix the value of the a 0 coefficient in (4.16).…”

“…Apart from their general importance for the evaluation of the QEF, to which we come back at the end of this paper, our results for the one-loop determinants of the various supergravity multiplets also have a more direct interpretation as logarithmic corrections to the leading Bekenstein-Hawking entropy. In this sense they are related to the logarithmic corrections to the entropy of asymptotically AdS 4 black holes derived in [16][17][18] using methods developed in [19][20][21][22], as well as to the field theoretic log N corrections to the leading large N expression calculated numerically in [16,23,24]. Our results however concern off-shell supergravity and should be interpreted in a slightly different context since the localization procedure requires some further input, such as the localization measure together with the aforementioned gravity and massive multiplet contributions, that is still missing.…”

Precision microstate counting for the entropy of wrapped M5-branes

“…One of the key problems plaguing a sub-leading understanding of N = 2 partition functions is that they are given in terms of solutions to certain Bethe-Ansatz equations, and there is no suitable framework to calculate the sub-leading contributions. Indeed, only a few partial results for sub-leading structures have been obtained and they involved substantial numerical efforts [22][23][24]. Let us emphasize that going beyond the leading order for the field theory partition function is not merely of academic interest; it promises to clarify intricate aspects of gravity on the holographic side.…”