Non-topological logarithmic corrections in minimal gauged supergravity

Abstract

We compute the logarithmic correction to the entropy of asymptotically AdS4 black holes in minimal $$ \mathcal{N} $$ N = 2 gauged supergravity. We show that for extremal black holes the logarithmic correction computed in the near horizon geometry agrees with the result in the full geometry up to zero mode contributions, thus clarifying where the quantum degrees of freedom lie in AdS spacetimes. In contrast to flat space, we observe that the logarithmic correction for supersymmetric black holes can be non-topological in AdS as it is controlled by additional four-derivative terms other than the Euler density. The available microscopic data and results in 11d supergravity indicate that the full logarithmic correction is topological, which suggests that the topological nature of logarithmic corrections could serve as a diagnosis of whether a low-energy gravity theory admits an ultraviolet completion.

Logarithmic correction to black hole entropy in universal low-energy string theory models

“…Note that the logarithmic prefactors (C, κ, η) in the formula (1.1) control the relative strengths of corresponding quantum corrections, which generally depend on the details of UV completion of the concerned low-energy gravity theory. Surprisingly, the logarithmic corrections and their prefactor C are special since they are entirely computable from the knowledge of only low-energy modes (IR data), i.e., massless fluctuations 3 running in one-loop [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. This fundamental feature makes them a strong infrared laboratory for the most active litmus test, i.e., any enumeration of black hole microstates inside the structure of string theory must agree with the logarithmic corrected entropy.…”

“…To date, pioneered by Ashoke Sen and collaborators and then followed by many other groups, the logarithmic corrections are mostly reported for the full Kerr-Newman family of black holes in EM theory [28][29][30]41] and all N ≥ 1 ungauged supergravity [25-27, 31, 33-35, 37-40, 42]. Few results are also available for AdS 4 black holes by Jeon et al [36] and David et al [43]. All this motivated us to the particular objective of this paper, i.e., computation of the logarithmic correction for all flat and AdS scalar-free black holes in the EMD and embedded supergravity theories.…”

“…For the logarithmic correction, one needs to extract and evaluate the exclusive "logarithmic term" from the one-loop quantum effective action part of massless fluctuations. To fulfill this purpose, the heat kernel method [71][72][73][74] is a practical and effective tool that has successfully reproduced correct results in all available cases [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Here the one-loop quantum effective actions are estimated by computing expansion coefficients of the heat kernel operator controlling all quadratic or one-loop fluctuations around a concerned black hole background.…”

“…The one-loop renormalization of cosmological and gravitational constants via a0(x) and a2(x) are ambiguous and scheme-dependent. For an example, refer to appendix D of [43]. 10 Note that the effective action (2.6) with massive m fluctuations turned on will read as W = ∓ 1 2 ln det(H + m 2 ), setting the heat trace expansion ∼ e −τ m 2 τ n− D 2 a2n(x) which never leads to ln AH in the one-loop correction terms via the integration (2.15).…”

“…In the large-charge limit 2 of black holes, the logarithmic correction is fully dominant over others. These logarithmic entropy corrections also turn out to be universal since they are inescapable in the structure of every quantum gravity, even via many different approaches like -Euclidean effective action method [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], quantum tunneling [21][22][23], conical singularity [17,18], Cardy formula [20], conformal anomaly [24], quantum geometry [19], non-local quantum gravity [44][45][46][47], etc. For a gravity model coupled to the higher-curvature terms beyond two-derivative, the expansion (1.1) in principle holds a similar form, except the BHAL gets modified into the Bekenstein-Hawking-Wald formula [50] by capturing the classical higher-derivative corrections to black hole entropy.…”