Logarithmic corrections to N ≥ 2 black hole entropy

Abstract:We compute the exact entropy of one-eighth and one-quarter BPS black holes in N = 8 and N = 4 string theory respectively. This includes all the N = 4 CHL models in both K3 and T 4 compactifications. The main result is a measure for the finite dimensional integral that one obtains after localization of supergravity on AdS 2 × S 2 . This measure is determined entirely by an anomaly in supersymmetric Chern-Simons theory on local AdS 3 and takes into account the contribution from all the supergravity multiplets. In Chern-Simons theory on compact manifolds, this is the anomaly that computes a certain one-loop dependence on the volume of the manifold. For one-eighth BPS black holes, our results are a first principles derivation of a measure proposed in arXiv:1111.1161, while in the case of one-quarter BPS black holes our result computes exactly all the perturbative or area corrections. Moreover, we argue that instantonic contributions can be incorporated and give evidence by computing the measure, which matches precisely the microscopics. Along with this, we find a unitary condition that truncates the answer to a finite sum of instantons in perfect agreement with a microscopic formula. Our results therefore solve a number of puzzles related to localization in supergravity and constitute a larger number of examples where holography can be shown to hold exactly.

“…9 Similar logarithmic corrections are found in [25,26] using properties of the supersymmetry algebra.…”

Section: N = 4 Supergravity and Attractor Backgroundsupporting

confidence: 57%

Section: Jhep07(2017)022mentioning

confidence: 99%

Exact Holography and Black Hole Entropy in N = 8 $$ \mathcal{N}=8 $$ and N = 4 $$ \mathcal{N}=4 $$ String Theory

Gomes

2017

“…For CHL models both d(Q) and its 4D(5D) supersymmetric black hole counterpart are known explicitly, and the agreement is remarkable (see appendix C for a quick review of this class of black holes). Logarithmic corrections have been computed as well for several other supersymmetric configurations [13,14] and using novel techniques in [15][16][17]. There are also very interesting results for non-extremal black holes [18,19].…”

Section: Jhep04(2017)057mentioning

confidence: 99%

“…where 15) and V m is the Hecke operator in (A.15). For now it is not important the details behind V m ; in what follows, the important observation is that φ 10,1 is the seed.…”

Section: The Igusa Cusp Form χ 10mentioning

confidence: 99%

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Siegel modular forms and black hole entropy

Belin

Castro

Gomes

et al. 2017

Abstract:We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form χ 10 in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case. We apply a similar method to extract the Fourier coefficients of other Siegel modular and paramodular forms, and we show that they could serve as candidates for other types of black holes. We investigate the growth of their coefficients, identifying the dominant contributions and the leading logarithmic corrections in various regimes. We also discuss similarities and differences to the behavior of χ 10 , and possible physical interpretations of such forms both from a microscopic and gravitational point of view.

Divergences and boundary modes in N = 8 $$ \mathcal{N}=8 $$ supergravity

Larsen

Lisbão

2016

Self Cite

We reconsider the one loop divergence of N = 8 supergravity in four dimensions. We compute the finite effective potential of N = 8 anti-deSitter supergravity and interpret it as logarithmic running of the cosmological constant. We show that quantum inequivalence between fields that are classically dual is due to boundary modes in AdS 4 . The boundary modes are important in global AdS 4 but not in thermal AdS 4 since these geometries have different Euler characteristic.