Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity

Abstract

The topologically twisted index for ABJM theory with gauge group U(N ) k × U(N ) −k has recently been shown, in the large-N limit, to reproduce the BekensteinHawking entropy of certain magnetically charged asymptotically AdS 4 black holes. We numerically study the index beyond the large-N limit and provide evidence that it contains a subleading logarithmic term of the form −1/2 log N . On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answer. We give some possible reasons for this apparent discrepancy.

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.…”

“…We are unable to fully determine the value of k 2 at the present stage, but our one-loop computations lead us to the expression 4) with g genus of the horizon, and we parametrize the as-of-yet unknown contribution of the additional gravity and massive multiplets by a 0 . On the field theory side, k 2 can be directly evaluated in the canonical ensemble as done in [16,23]. The above expansion follows from the quantum entropy function formalism and therefore naturally makes use of the scales of AdS 2 and the internal space.…”

Precision microstate counting for the entropy of wrapped M5-branes

“…Doing so will advance the inherent promise of the AdS/CFT correspondence of providing a non-perturbative path to quantum gravity in asymptotically AdS spacetimes. Indeed, for a class of black holes some progress has been reported in [23] after preliminary explorations in [22,92].…”

“…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.…”