Logarithmic corrections to twisted indices from the quantum entropy function

We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D N ≥ 2 supergravity theories. This branch corresponds to finite temperature black holes whose extremal limit does not preserve supersymmetry, such as the D0 − D6 system in string theory. Starting from a black hole in minimal Kaluza-Klein theory, we discuss in detail its embedding into N = 8, 6, 4, 2 supergravity, its spectrum of quadratic fluctuations in all these environments, and the resulting quantum corrections. We find that the c-anomaly vanishes only when N ≥ 6, in contrast to the BPS branch where c vanishes for all N ≥ 2. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.

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confidence: 90%

Logarithmic corrections to black hole entropy: the non-BPS branch

Castro

Godet

Larsen

et al. 2018

“…These logarithmic corrections are universal in this sense that they appear in any generic theory of gravity. But c does not have the same sort of universality: it can be determined only from low energy modes, i.e., the spectrum of massless fields present in the theory, and are unconcerned about UV completion of the theory [3][4][5][6][7][8][9][10][11][12][13]. These correction terms are important as they provide us with the non-trivial information about the microstates of the black holes and hence providing a valuable testing ground for any candidate theory of quantum gravity.…”

Section: Introductionmentioning

confidence: 99%

Seeley-DeWitt coefficients in $$ \mathcal{N} $$ = 2 Einstein-Maxwell supergravity theory and logarithmic corrections to $$ \mathcal{N} $$ = 2 extremal black hole entropy

Karan

Banerjee

Panda

2019

We investigate the heat kernel method for one-loop effective action following the Seeley-DeWitt expansion technique of heat kernel with Seeley-DeWitt coefficients. We also review a general approach of computing the Seeley-DeWitt coefficients in terms of background or geometric invariants. We, then consider the Einstein-Maxwell theory embedded in minimal N = 2 supergravity in four dimensions and compute the first three Seeley-DeWitt coefficients of the kinetic operator of the bosonic and the fermionic fields in an arbitrary background field configuration. We find the applications of these results in the computation of logarithmic corrections to Bekenstein-Hawking entropy of the extremal Kerr-Newman, Kerr and Reissner-Nordström black holes in minimal N = 2 Einstein-Maxwell supergravity theory following the quantum entropy function formalism.

“…Gravitational investigations of similarly twisted the quarter-BPS counting functions were presented in e.g. [52,[60][61][62], but none of these studies employ the localization techniques used here. Indeed, even the untwisted quarter-BPS index is not completely understood from this perspective; see [57][58][59]63] for progress towards deriving and interpreting a Rademacher-type expansion for the quarter-BPS spectrum.…”

Section: Discussionmentioning

confidence: 99%

Exact half-BPS black hole entropies in CHL models from Rademacher series

Nally¹

2019

The microscopic spectrum of half-BPS excitations in toroidally compactified heterotic string theory has been computed exactly through the use of results from analytic number theory. Recently, similar quantities have been understood macroscopically by evaluating the gravitational path integral on the M-theory lift of the AdS 2 near-horizon geometry of the corresponding black hole. In this paper, we generalize these results to a subset of the CHL models, which include the standard compactification of IIA on K3 × T 2 as a special case. We begin by developing a Rademacher-like expansion for the Fourier coefficients of the partition functions for these theories, which are modular forms for congruence subgroups. We then interpret these results in a macroscopic setting by evaluating the path integral for the reduced-rank N = 4 supergravities described by these CFTs.