Search

We investigate equivariant localization of the gravitational on-shell action in odd dimensions, focusing on five-dimensional ungauged supergravity. We analyze the conditions for cancellation of boundary terms, so that the full action integral is given in terms of the odd-dimensional analog of the nuts and bolts of Gibbons-Hawking. We specialize to supersymmetric configurations with an additional ${\rm U}(1)$ symmetry preserving the supercharge and provide a formula for the localized on-shell action. We construct asymptotically flat Euclidean supersymmetric non-extremal solutions with two independent rotations and an arbitrary number of electric charges, providing black hole saddles of the gravitational path integral that computes a supersymmetric index, and evaluate their action equivariantly. We find that these Euclidean saddles interpolate between supersymmetric extremal black holes and two-center horizonless microstate geometries. The interpolation involves dialing the temperature and implementing different analytic continuations. The corresponding on-shell action does not depend on temperature but is affected by the analytic continuations., Comment: 65 pages; v2: clarifications about the role of the solutions as saddles of the index added, minor corrections, references added

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.

A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by 't Hooft anomalies and to single out a large-$N$ saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS$_5$. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the 't Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-$N$ expansion. Then we focus on a specific model dual to $\mathbb{C}^3/\mathbb{Z}_\nu$ quiver gauge theories, where the 't Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS$_5$ radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes., Comment: 64 pages, 1 figure; v2: minor changes, references added, matched published version

We find solutions of the heterotic string effective action describing the first-order $\alpha'$ corrections to two-charge black holes at finite temperature. Making explicit use of these solutions, we compute the corrections to the thermodynamic quantities: temperature, chemical potentials, mass, charges and entropy. We check that the first law of black hole mechanics is satisfied and that the thermodynamics agrees with the one extracted from the Euclidean on-shell action. Finally, we show that our results are in agreement with the corrections for the thermodynamics recently predicted by Chen, Maldacena and Witten., Comment: 27 pages; v2: citations added

We address some issues in higher-derivative gauged supergravity with Chern-Simons terms, focusing on the five-dimensional case. We discuss the variational problem with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald's formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and U(1) gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between Noether charges and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS$_5$ from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the entropy as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory., Comment: 39 pages

We consider type IIB compactifications on a general 4D group manifold with different types of possible spacetime filling O-planes and the corresponding D-branes parallel to them. Once fluxes allowed by the associated orientifold projection are included, a 6D $\mathcal{N}=(1,1)$ gauged supergravity is obtained. In this paper we show how the consistent coupling to dynamical open strings living on the spacetime filling D-branes may be captured by the inclusion of extra vector multiplets and extra embedding tensor deformations on the gauged supergravity side. As a result, the quadratic constraints on the embedding tensor consistently reproduce the source corrected 10D Bianchi identities. Furthermore, the field strength modifications induced by the open string sector could potentially be understood as U-dual versions of the Green-Schwarz terms. Finally, the entire scalar potential of the theory exactly matches the one obtained from reduction of the bulk action plus the source contributions., Comment: 45 pages, 1 figure

We compute the first-order $\alpha'$ corrections of the non-extremal Strominger-Vafa black hole and its non-supersymmetric counterparts in the framework of the Bergshoeff-de Roo formulation of the heterotic superstring effective action. The solution passes several tests: its extremal limit is the one found in an earlier publication and the effect of a T duality transformation on it is another solution of the same form with T dual charges. We compute the Hawking temperature and Wald entropy showing that they are related by the first law and Smarr formula. On the other hand, these two contain additional terms in which the dimensionful parameter $\alpha'$ plays the role of thermodynamical variable., Comment: Latex2e file, 53 pages, 7 figures; v2: references added

We consider a broad family of higher-derivative extensions of four-dimensional Einstein gravity and study the multipole moments of rotating black holes therein. We carefully show that the various definitions of multipoles carry over from general relativity, and compute these multipoles for higher-derivative Kerr using the ACMC expansion formalism. We obtain the mass $M_{n}$ and current $S_{n}$ multipoles as a series expansions in the dimensionless spin; in some cases we are able to resum these series into closed-form expressions. Moreover, we observe the existence of intriguing relations between the corrections to the parity-odd multipoles $S_{2n}\neq 0$ and $M_{2n+1}\neq 0$ that break equatorial symmetry, and the parity-preserving corrections that only modify $S_{2n+1}$ and $M_{2n}$. Further, we comment on the higher-derivative corrections to multipole ratios for Kerr, and we discuss the phenomenological implications of the corrections to the multipole moments for current and future gravitational wave experiments., Comment: 31 pages + Appendix, 13 figures, Mathematica notebook with all expansions used in the paper. Updated to match published version

We study four-derivative corrections to five-dimensional minimal gauged supergravity. We evaluate the on-shell action of the AdS$_5$ black hole solution with two independent angular momenta and one electric charge at linear order in the corrections. After imposing supersymmetry, we are able to recast the action in terms of the supersymmetric chemical potentials and match the result obtained from the dual superconformal index on the second sheet. To achieve this, we exploit the freedom to implement field redefinitions to recast the action in a much simpler form, as well as the fact that the two-derivative solution is enough. We use the on-shell action to determine the corrections to the black hole thermodynamics, including those to the entropy and the charges. We then specialize to the supersymmetric and extremal case and find a simple expression for the microcanonical entropy. In particular, for the case with one independent angular momentum the corrections are entirely encoded in the dual superconformal anomaly coefficients. We corroborate this result for the entropy by constructing the corrected near-horizon solution and applying Wald's formula., Comment: 53 pages; v2: new results on general angular momenta and Legendre transform of the susy on-shell action added, clarifications added, typos fixed, references added; v3: published version

We compute the first-order $\alpha'$ corrections to well-known families of heterotic multi-center black-hole solutions in five and four dimensions. The solutions can be either supersymmetric or non-supersymmetric, depending on the relative sign between two of the black-hole charges. For both cases, we find that the equilibrium of forces persists after including the $\alpha'$ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation., Comment: Abstract, introduction and conclusions rewritten with a different point of view. The multi-center black-hole solutions found and the main results remain unchanged. 42 pages, 7 figures

We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in $\alpha'$ with, respectively, 3 and 4 charges of arbitrary signs. For a particular choice of the relative signs of these charges the solutions are supersymmetric, but other signs give rise to non-supersymmetric extremal black holes. Although at zeroth order all these solutions are formally identical, we show that the $\alpha'$ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic $\mathcal{O}(\alpha')$ solutions and we compute their charges, masses and entropies and check that they are invariant under $\alpha'$-corrected T-duality transformations. The masses of some of these black holes are corrected in a complicated way, but we show that the shift is always negative, in agreement with the Weak Gravity Conjecture. Our formula for the corrected entropy of the four-dimensional black holes generalizes previous results obtained from the entropy function method, as we consider a more general way in which supersymmetry can be broken., Comment: 58 pages, 1 figure, version to be sent to JHEP (improved presentation and typos fixed)

We revisit the four-dimensional theory of gravity that arises from string theory with higher-derivative corrections. By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in $\alpha'$, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities. Thus, the actual string gravity is a generalization of the well-studied Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons models. Using this action we compute the stringy corrections to the Kerr geometry and we obtain, for the first time, the corrections to the entropy of the Kerr black hole at order $\alpha'^2$. We check that the first law of black hole mechanics is satisfied and discuss several properties of the solution. Our results suggest that there exist black hole solutions with $J>M^2$ and therefore the extremal ratio $J/M^2$ must be modified positively., Comment: 16 pages, 4 figures, double column. v2: references, footnotes 1 and 10 and a comment on consistency of the truncation have been added. Version sent to PRD

We review and extend results on higher-curvature corrections to different configurations describing a superposition of heterotic strings, KK monopoles, solitonic 5-branes and momentum waves. Depending on which sources are present, the low-energy fields describe a black hole, a soliton or a naked singularity. We show that this property is unaltered when perturbative higher-curvature corrections are included, provided the sources are fixed. On the other hand, this character may be changed by appropriate introduction (or removal) of sources regardless of the presence of curvature corrections, which constitutes a non-perturbative modification of the departing system. The general system of multicenter KK monopoles and their 5-brane charge induced by higher-curvature corrections is discussed in some detail, with special attention paid to the possibility of merging monopoles. Our results are particularly relevant for small black holes (Dabholkar-Harvey states, DH), which remain singular after quadratic curvature corrections are taken into account. When there are four non-compact dimensions, we notice the existence of a black hole with regular horizon whose entropy coincides with that of the DH states, but the charges and supersymmetry preserved by both configurations are different. A similar construction with five non-compact dimensions is possible, in this case with the same charges as DH, although it fails to reproduce the DH entropy and supersymmetry. No such configuration exists if $d>5$, which we interpret as reflecting the necessity of having a 5-brane wrapping the compact space., Comment: 56 pages, 1 figure; v2: minor changes to match published version

We compute the first-order $\alpha'$-corrections to a general family of supersymmetric heterotic backgrounds which describes a rotating superposition of a fundamental string and a momentum wave. We focus on a particular solution within this family that gives raise, upon dimensional reduction to five dimensions, to a black ring with two charges and one dipole that has a singular horizon with vanishing area in the supergravity approximation, better known as small black ring. We show that the singularity at the horizon persists even after the first-order $\alpha'$-corrections have been taken into account. This implies, contrary to what has been argued in the literature, that higher-derivative corrections do not resolve the singular horizon of the 5-dimensional small black ring, at least at first-order in $\alpha'$., Comment: 25 pages, 1 figure; v2: supplemental material and further discussions have been included. It matches the published version

We argue that the conjectural relation between the subleading term in the small-squashing expansion of the free energy of general three-dimensional CFTs on squashed spheres and the stress-tensor three-point charge $t_4$ proposed in arXiv:1808.02052: $F_{\mathbb{S}^3_{\varepsilon}}^{(3)}(0)=\frac{1}{630}\pi^4 C_{\scriptscriptstyle T} t_4$, holds for an infinite family of holographic higher-curvature theories. Using holographic calculations for quartic and quintic Generalized Quasi-topological gravities and general-order Quasi-topological gravities, we identify an analogous analytic relation between such term and the charges $t_2$ and $t_4$ valid for five-dimensional theories: $F_{\mathbb{S}^5_{\varepsilon}}^{(3)}(0)=\frac{2}{15}\pi^6 C_{ \scriptscriptstyle T} \left[1+\frac{3}{40} t_2+\frac{23}{630} t_4\right]$. We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement., Comment: 52 pages, 2 figures

We present new supersymmetric black-hole solutions of the 4- and 5-dimensional gauged supergravity theories that one obtains by dimensional reduction on $T^{5}$ and $T^{6}$ of Heterotic supergravity with a triplet of Yang-Mills fields. The new ingredient of our solutions is the presence of dyonic non-Abelian fields which allows us to obtain a generalization of the BMPV black hole with two independent angular momenta and the first example of a supersymmetric, rotating, asymptotically-flat black hole with a regular horizon in 4 dimensions., Comment: 41 pages. Version accepted in JHEP

We compute the most general leading-order correction to Kerr solution when the Einstein-Hilbert action is supplemented with higher-derivative terms, including the possibility of dynamical couplings controlled by scalars. The model we present depends on five parameters and it contains, as particular cases, Einstein-dilaton-Gauss-Bonnet gravity, dynamical Chern-Simons gravity and the effective action coming from Heterotic Superstring theory. By solving the corrected field equations, we find the modified Kerr metric that describes rotating black holes in these theories. We express the solution as a series in the spin parameter $\chi$, and we show that including enough terms in the expansion we are able to describe black holes with large spin. For the computations in the text we use an expansion up to order $\chi^{14}$, which is accurate for $\chi<0.7$, but we provide as well a Mathematica notebook that computes the solution at any given order. We study several properties of the corrected black holes, such as geometry of the horizon, ergosphere, light rings and scalar hair. Some of the corrections violate parity, and we highlight in those cases plots of horizons and ergospheres without $\mathbb{Z}_{2}$ symmetry., Comment: v3: The equations 4.41-4.43 for the lightring frequencies have been amended. These formulas were incorrect in the previous versions due to an error when translating the results to the LaTeX file (the error does not propagate to other results). For all the rest, this version matches the one published in JHEP

Small black holes in string theory are characterized by a classically singular horizon with vanishing Bekenstein-Hawking entropy. It has been argued that higher-curvature corrections resolve the horizon and that the associated Wald entropy is in agreement with the microscopic degeneracy. In this note we study the heterotic two-charge small black hole and question this result, which we claim is caused by a misidentification of the fundamental constituents of the system studied when higher-curvature interactions are present. On the one hand, we show that quadratic curvature corrections do not solve the singular horizon of small black holes. On the other, we argue that the resolution of the heterotic small black hole reported in the literature involves the introduction of solitonic 5-branes, whose asymptotic charge vanishes due to a screening effect induced by the higher-curvature interactions, and a Kaluza-Klein monopole, whose charge remains unscreened., Comment: 7 pages; v2 restructured exposition with additional clarifying comments and information, same scientific content

We study the first-order in $\alpha'$ corrections to 4-charge black holes (with the Reissner-Nordstr\"om black hole as a particular example) beyond the near-horizon limit in the Heterotic Superstring effective action framework. The higher-curvature terms behave as delocalized sources in the equations of motion and in the Bianchi identity of the 3-form. For some charges, this introduces a shift between their values measured at the horizon and asymptotically. Some of these corrections and their associated charge shifts, but not all of them, can be canceled using appropriate SU$(2)$ instantons for the heterotic gauge fields. The entropy, computed using Wald's formula, is in agreement with the result obtained via microstate counting when the delocalized sources are properly taken into account., Comment: 46 pages

We study the first-order $\alpha'$ corrections to the singular 4-dimensional massless stringy black holes studied in the nineties in the context of the Heterotic Superstring. We show that the $\alpha'$ corrections not only induce a non-vanishing mass and give rise to an event horizon, but also eliminate the singularity giving rise to a regular spacetime whose global structure includes further asymptotically flat regions in which the spacetime's mass is positive or negative. We study the timelike and null geodesics and their effective potential, showing that the spacetime is geodesically complete. We discuss the validity of this solution, arguing that the very interesting and peculiar properties of the solution are associated to the negative energy contributions coming from the terms quadratic in the curvature. As a matter of fact, the 10-dimensional configuration is singular. We extract some general lessons on attempts to eliminate black-hole singularities by introducing terms of higher order in the curvature., Comment: 5 pages, 2 figures

We compute explicitly the first-order in $\alpha'$ corrections to a family of solutions of the Heterotic Superstring effective action that describes fundamental strings with momentum along themselves, parallel to solitonic 5-branes with Kaluza-Klein monopoles (Gibbons-Hawking metrics) in their transverse space. These solutions correspond to 4-charge extremal black holes in 4 dimensions upon dimensional reduction on $\mathrm{T}^{6}$. We show that some of the $\alpha'$ corrections can be cancelled by introducing solitonic $\mathrm{SU}(2)\times \mathrm{SU}(2)$ Yang-Mills fields, and that this family of $\alpha'$-corrected solutions is invariant under $\alpha'$-corrected T-duality transformations. We study in detail the mechanism that allows us to compute explicitly these $\alpha'$ corrections for the ansatz considered here, based on a generalization of the 't Hooft ansatz to hyperK\"ahler spaces., Comment: v2: typos corrected, references added

We construct supersymmetric solutions of theories of gauged $\mathcal{N}=1,d=5$ supergravity coupled to vector multiplets with a $\mathrm{U}(1)_{\rm R}$ Abelian (Fayet-Iliopoulos) gauging and an independent SU$(2)$ gauging associated to an $\mathrm{SU}(2)$ isometry group of the Real Special scalar manifold. These theories provide minimal supersymmetrizations of 5-dimensional SU$(2)$ Einstein-Yang-Mills theories with negative cosmological constant. We consider a minimal model with these gauge groups and the "magic model" based on the Jordan algebra $\bf{J}_{3}^\mathbb{C}$ with gauge group $\mathrm{SU}(3)\times\mathrm{U}(1)_{\rm R}$, which is a consistent truncation of maximal $\mathrm{SO}(6)$-gauged supergravity in $d=5$ and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual $\mathrm{SU}(2)$ instantons, some of which asymptote to AdS$_{5}$ and some of which are very small, supersymmetric, deformations of AdS$_{5}$. We also show how some of those solutions can be embedded in Romans' $\mathrm{SU}(2)\times\mathrm{U}(1)$-gauged half-maximal supergravity, which was obtained by Lu, Pope and Tran by compactification of the Type IIB Superstring effective action. This provides another way of uplifting those solutions to 10 dimensions.

Einsteinian cubic gravity provides a holographic toy model of a nonsupersymmetric CFT in three dimensions, analogous to the one defined by Quasi-topological gravity in four. The theory admits explicit non-hairy AdS$_4$ black holes and allows for numerous exact calculations, fully nonperturbative in the new coupling. We identify several entries of the AdS/CFT dictionary for this theory, and study its thermodynamic phase space, finding interesting new phenomena. We also analyze the dependence of R\'enyi entropies for disk regions on universal quantities characterizing the CFT. In addition, we show that $\eta/s$ is given by a non-analytic function of the ECG coupling, and that the existence of positive-energy black holes strictly forbids violations of the KSS bound. Along the way, we introduce a new method for evaluating Euclidean on-shell actions for general higher-order gravities possessing second-order linearized equations on AdS$_{(d+1)}$. Our generalized action involves the very same Gibbons-Hawking boundary term and counterterms valid for Einstein gravity, which now appear weighted by the universal charge $a^*$ controlling the entanglement entropy across a spherical region in the CFT dual to the corresponding higher-order theory., Comment: 59 pages, 7 figures, 1 table; v4: typos fixed

We consider self-dual Yang-Mills instantons in 4-dimensional Kaehler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We then search for solutions of this equation in 3-dimensional metrics foliated by 2-dimensional spheres, hyperboloids or planes in the case in which the gauge group coincides with the isometry group of the metric (SO(3), SO(1,2) and ISO(2), respectively). Using a generalized hedgehog ansatz the Bogomol'nyi quations reduce to a simple differential equation in the radial variable which admits a universal solution and, in some cases, a particular one, from which one finally recovers instanton solutions in the original Kaehler space. We work out completely a few explicit examples for some Kaehler spaces of interest., Comment: Latex2e file, 16 pages, no figures

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum., Comment: 33 pages. v2: typos corrected