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Two universal predictions of general relativity are the propagation of gravitational waves of large momentum along null geodesics and the isospectrality of quasinormal modes in many families of black holes. In extensions of general relativity, these properties are typically lost: quasinormal modes are no longer isospectral and gravitational wave propagation is no longer geodesic and it exhibits birefringence -- polarization-dependent speed. We study these effects in an effective-field-theory extension of general relativity with up to eight-derivative terms and show that there is a unique Lagrangian that has a non-birefringent dispersion relation for gravitational waves and isospectral quasinormal modes in the eikonal limit. We argue that both properties are related through a generalized correspondence between eikonal quasinormal modes and unstable photon-sphere orbits. These properties define a special class of theories that we denote as isospectral effective field theories. We note that the lowest-order isospectral correction to general relativity coincides with the quartic-curvature correction arising from type II string theory, suggesting that isospectrality might be a key feature of quantum gravity., Comment: 10 pages; v2: references added, appendix extended. Version sent to journal

We study gravitational perturbations on the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. We find a decoupled modified Teukolsky equation that rules the gravitational perturbations and that separates into an angular and a radial equation. The angular equation leads to a deformation of the spin-weighted spheroidal harmonics, while the radial equation takes the same form as in Kerr except for a modification of the angular separation constants. We provide a detailed analysis of the corrections to these angular separation constants and find analytic results for axisymmetric modes as well as in the eikonal limit. As an application, we reproduce recent results that show that extremal Kerr black holes in higher-derivative gravity become singular under certain deformations and extend them by including parity-breaking corrections, which we show lead to the same effect. Finally, we obtain constraints on the form of the full modified Teukolsky radial equation by demanding that it has the right near-horizon limit. These results serve as an stepping stone towards the study of quasinormal modes of near-extremal black holes in higher-derivative extensions of GR., Comment: 44 pages, 2 figures, ancillary Mathematica notebook included; v2:references added, version sent to journal; v3:published version

Higher-derivative corrections in the AdS/CFT correspondence allow us to capture finer details of the dual CFT and to explore the holographic dictionary beyond the infinite N and strong coupling limits. Following an effective field theory approach, we investigate extremal AdS black hole solutions in five-dimensional supergravity with higher-derivative corrections. We provide a general analysis of near-horizon geometries of rotating extremal black holes and show how to obtain their corresponding charges and chemical potentials. We discuss the near-horizon solutions of the two-derivative theory, which we write using a novel parametrization that eases our computation of the higher-derivative corrections. The charges and thermodynamic properties of the black hole are computed while clarifying the ambiguities in their definitions. The charges and potentials turn out to satisfy a near-horizon version of the first law of thermodynamics whose interpretation we make clear. In the supersymmetric case, the results are shown to match the field theory prediction as well as previous results obtained from the on-shell action., Comment: 41 pages and 1 figure; ancillary Mathematica notebook with corresponding higher derivative results

Understanding how the thermodynamic properties of a black hole are modified when probed by D-branes is an important problem in AdS/CFT. This work focuses on a recently proposed black hole/D3-brane system in AdS$_5\times$S$^5$, which is dual to four-dimensional N=4 SYM in the presence of a two-dimensional surface defect. The Laplace transform that extracts the asymptotic growth of states in this defect CFT naturally defines a thermodynamic approach in the gravitational side of the duality for which charges and entropy are real. Studying the superconformal defect index in a large-charge expansion for all values of~$N$, we compute the leading correction to the entropy of the combined system, which matches precisely with its gravity counterpart., Comment: 24 pages, 3 figures

We study the logarithmic corrections to various CFT partition functions in the context of the AdS$_4$/CFT$_3$ correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordstr\"om black holes in AdS$_4$. Our results also have important implications for effective field theory coupled to gravity in AdS$_4$ and for the existence of scale-separated AdS$_4$ vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields., Comment: v1: 87 pages, 10 tables; v2: Seeley-de Witt coefficients in the presence of non-minimal couplings dictated by supersymmetry are newly addressed in section 5 and following places

We construct a general asymptotically locally AdS$_7$ stationary black hole solution of 7d maximal gauged supergravity with three angular momenta and two electric charges. When embedded in 11d supergravity the black hole describes the backreaction of $N$ coincident rotating M5-branes. We study the thermodynamic properties of the black hole and present explicit expressions for its entropy, energy, electric charges, and angular momenta. We show that in the supersymmetric limit of the solution its entropy and on-shell action precisely agree with the result for the path integral of the holographically dual 6d $\mathcal{N}=(2,0)$ SCFT on $S^1\times S^5$ to leading order in the large $N$ limit., Comment: v1: 32 pages; v2: minor revisions including corrected typos, attached a Mathematica Notebook providing various expressions in the paper

We study the flow equations for BPS black holes in $\mathcal{N} = 2$ five-dimensional gauged supergravity coupled to any number of vector multiplets via FI couplings. We develop the Noether-Wald procedure in this context and exhibit the conserved charges as explicit integrals of motion, in the sense that they can be computed at any radius on the rotating spacetime. The boundary conditions needed to solve the first order differential equations are discussed in great detail. We extremize the entropy function that controls the near horizon geometry and give explicit formulae for all geometric variables at their supersymmetric extrema. We have also considered a complexification of the near-horizon variables that elucidates some features of the theory from the near-horizon perspective.

We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with $\alpha'$ corrections and of a cubic-curvature extension of general relativity. By analyzing the near-horizon extremal geometry of these black holes, we are able to compute the Iyer-Wald entropy as well as the angular momentum via generalized Komar integrals. In the case of the stringy corrections, we obtain the physically relevant relation $S(J)$ at order $\alpha'^2$. On the other hand, the cubic theories, which are chosen as Einsteinian cubic gravity plus a new odd-parity density with analogous features, possess special integrability properties that enable us to obtain exact results in the higher-derivative couplings. This allows us to find the relation $S(J)$ at arbitrary orders in the couplings and even to study it in a non-perturbative way. We also extend our analysis to the case of the extremal Kerr-(A)dS black hole., Comment: 33 pages+appendices, one figure

T-duality has been shown to constrain the higher derivative corrections of string theory. We revisit the problem of understanding the T-duality constraints imposed on the $\alpha'$ corrections using the language of a torsionful connection. We find a convenient way to express the $O(d,d)$ invariants in terms of linear combinations of the metric and B-field for general $d$-dimensional torus compactifications, which we then use to revisit the heterotic and bosonic ten-dimensional string action at order $\alpha'$. We also comment on the four-point functions for corrections of order $\alpha'^3$ in the type II string.

We compute the logarithmic correction to the entropy of asymptotically AdS$_4$ black holes in minimal ${\cal N}=2$ 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., Comment: 63 pages

We examine the structure of higher-derivative string corrections under a cosmological reduction and make connection to generalized geometry and T-duality. We observe that, while the curvature $R^\mu{}_{\nu\rho\sigma}(\Omega_+)$ of the generalized connection with torsion, $\Omega_+=\Omega+\frac{1}{2}H$, is an important component in forming T-duality invariants, it is necessarily incomplete by itself. We revisit the tree-level $\alpha'R^2$ corrections to the bosonic and heterotic string in the language of generalized geometry and explicitly demonstrate that additional $H$-field couplings are needed to restore T-duality invariance. We also comment on the structure of the T-duality completion of tree-level $\alpha'^3R^4$ in the type II string., Comment: 32 pages

We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS$_5$ black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined, on the field theory side, by the superconformal index and the refined topologically twisted index of $\mathcal{N}=4$ supersymmetric Yang-Mills theory, respectively. We read off the logarithmic correction from those field-theoretic partition functions. On the gravity side, we take the near-horizon limit and apply the Kerr/CFT correspondence whose associated charged Cardy formula describes the degeneracy of states at subleading order and determines the logarithmic correction to the entropy. We find perfect agreement between these two approaches. Our results provide a window into precision microstate counting and demonstrate the efficacy of low-energy, symmetry-based approaches such as the Kerr/CFT correspondence for asymptotically AdS black objects under certain conditions., Comment: 31 pages, no figures; v2: published version in JHEP, more details added in Sec. 2.2, 2.4, and 2.5, the main results updated

We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS$_4$ electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to compute the left and right central charges. We also use hidden conformal symmetry of the near-horizon geometry to compute the Frolov-Thorne temperatures. From the results of the near-extremal AdS$_4$ black hole entropy, we provide a microscopic foundation for Hawking radiation., Comment: 25 pages, 2 figures; v2: Sec. 2.1 and Sec. 2.3 updated; v3: published version in JHEP, minor changes in Sec. 2 and 3

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta, and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS$_{4, 5, 6, 7}$ BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions., Comment: 53 pages, 1 table, 1 figure; v2: typos corrected, references and new acknowledgements added, JHEP version

We compute the one-loop effective action of string configurations embedded in $AdS_4\times\mathbb{CP}^3$ which are dual to $\frac{1}{6}$-BPS latitude Wilson Loops in the ABJM theory. To avoid ambiguities in the string path integral we subtract the $\frac{1}{2}$-BPS case. The one-loop determinants are computed by Fourier-decomposing the two dimensional operators and then using the Gel'fand-Yaglom method. We comment on various aspects related to the regularization procedure, showing the cancellation of a hierarchy of divergences. After taking into account an IR anomaly from a change in topology, we find a precise agreement with the field theory result known from supersymmetric localization., Comment: 14 pages; v2: references added, comment about boundary conditions added

Representation of analytic functions as convergent series in Jacobi polynomials $P_n^{(a,b)}$ is reformulated using a unified approach for almost all complex $a, b$. The coefficients of the series are given as usual integrals in the classical case (when $\Re a, \Re b >-1$), or by the Hadamard principal part of these integrals when they diverge. As an application it is shown that inhomogeneous hypergeometric equations do generically have a unique solution which is analytic at both singular points in the complex plane.