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Pablo A. Cano

Publications and source records attributed to Pablo A. Cano.

At least 73 records · Page 4Linked to original sources
arXiv2020

Partition functions on slightly squashed spheres and flux parameters

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: $F_{\mathbb{S}^3_{\varepsilon}}^{(3)}(0)=\frac{1}{630}π^4 C_{\scriptscriptstyle T} t_4$, 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: $F_{\mathbb{S}^5_{\varepsilon}}^{(3)}(0)=\frac{2}{15}π^6 C_{ \scriptscriptstyle T} \left[1+\frac{3}{40} t_2+\frac{23}{630} t_4\right]$. We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.

hep-th↗
arXiv2019

Higher-Curvature Gravity, Black Holes and Holography

Recently, the identification of new higher-curvature interactions known as Einsteinian cubic gravity (ECG) and Generalized quasi-topological gravities (GQGs) has allowed for important advances in the study of black hole solutions and holographic applications of higher-order gravity. These theories are characterized by having second-order linearized equations on maximally symmetric background and by possessing static, spherically symmetric (SSS) black hole solutions satisfying $g_{tt}g_{rr}=-1$, and whose thermodynamic properties can be studied analytically in a fully non-perturbative fashion. In the first part of this thesis, we perform a detailed analysis of the weak-field limit of $\mathcal{L}($Riemann$)$ theories and of the condition $g_{tt}g_{rr}=-1$ on SSS solutions, and we review the construction of ECG and Generalized quasi-topological gravities. In addition, we show that GQGs could serve as building blocks to construct the most general EFT for gravity. In the second part we study the non-perturbative corrections to the asymptotically flat Schwarzschild black hole in $D=4$. We obtain closed exact expressions for the thermodynamic properties of spherically symmetric black holes with an arbitrary number of higher-curvature terms. We find that, quite generally, the higher-curvature corrections make the specific heat of these black holes positive below certain mass, and hence black holes take an infinite time to evaporate and the final "Hawking explosion" is avoided. In the last part we study asymptotically AdS black holes and Euclidean-AdS-Taub-NUT solutions and we establish various entries of the holographic dictionary of $D=4$ ECG. We illustrate the power of holographic higher-order gravities by obtaining a relation for the free energy of CFTs on squashed spheres, which we conjecture to be valid for arbitrary CFTs.

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arXiv2019

All higher-curvature gravities as Generalized quasi-topological gravities

Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity characterized by the existence of non-hairy generalizations of the Schwarzschild black hole which satisfy $g_{tt}g_{rr}=-1$, as well as for having second-order linearized equations around maximally symmetric backgrounds. In this paper we provide strong evidence that any gravitational effective action involving higher-curvature corrections is equivalent, via metric redefinitions, to some GQTG. In the case of theories involving invariants constructed from contractions of the Riemann tensor and the metric, we show this claim to be true as long as (at least) one non-trivial GQTG invariant exists at each order in curvature ---and extremely conclusive evidence suggests this is the case in general dimensions. When covariant derivatives of the Riemann tensor are included, the evidence provided is not as definitive, but we still prove the claim explicitly for all theories including up to eight derivatives of the metric as well as for terms involving arbitrary contractions of two covariant derivatives of the Riemann tensor and any number of Riemann tensors. Our results suggest that the physics of generic higher-curvature gravity black holes is captured by their GQTG counterparts, dramatically easier to characterize and universal. As an example, we map the gravity sector of the Type-IIB string theory effective action in AdS$_5$ at order $\mathcal{O}({α^{\prime}}^3)$ to a GQTG and show that the thermodynamic properties of black holes in both frames match.

hep-th↗
arXiv2019

$α'$ corrections of Reissner-Nordström black holes

We study the first-order in $α'$ corrections to non-extremal 4-dimensional dyonic Reissner-Nordström (RN) black holes with equal electric and magnetic charges in the context of Heterotic Superstring effective field theory (HST) compactified on a $T^{6}$. The particular embedding of the dyonic RN black hole in HST considered here is not supersymmetric in the extremal limit. We show that, at first order in $α'$, consistency with the equations of motion of the HST demands additional scalar and vector fields become active, and we provide explicit expressions for all of them. We determine analytically the position of the event horizon of the black hole, as well as the corrections to the extremality bound, to the temperature and to the entropy, checking that they are related by the first law of black-hole thermodynamics, so that $\partial S/\partial M=1/T$. We discuss the implications of our results in the context of the Weak Gravity Conjecture, clarifying that entropy corrections for fixed mass and charge at extremality do not necessarily imply corrections to the extremal charge-to-mass ratio.

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arXiv2019

Extremal Rotating Black Holes in Einsteinian Cubic Gravity

We obtain new solutions of Einsteinian cubic gravity coupled to a Maxwell field that describe the near-horizon geometry of charged and rotating black holes. We show that the AdS$_2\times\mathbb{S}^2$ near-horizon geometry of Reissner-Nordström black holes receives no corrections, but deviations with respect to the extremal Kerr-Newman solution appear as we turn on the angular momentum. We construct the profile of these corrected geometries using both numerical methods and slowly-spinning expansions, but we also find additional solutions that do not reduce to AdS$_2\times\mathbb{S}^2$ geometries in any limit and that do not have a counterpart in Einstein gravity. Quite remarkably, we are able to obtain closed-form exact expressions for the area and Wald's entropy of all of these solutions, and using this result, we analyze the phase space of extremal back holes in this theory. To the best of our knowledge, this is the first time the entropy of a rotating black hole in higher-order gravity has been exactly computed.

hep-th↗
arXiv2019

On the extremality bound of stringy black holes

A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account. Since these corrections become more relevant in the low-mass regime, this would allow the decay of extremal black holes in terms of energy and charge conservation. Evidence in this direction has been mainly given in the context of corrections to Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass ratio of some dyonic extremal black holes explicitly embedded in the heterotic string effective theory. We find that modifications of the extremality bound depend on the solution considered, with the charge-to-mass ratio remaining unchanged or deviating positively from one. Additionally, we observe that the introduction of the higher-curvature terms increases the Wald entropy in all cases considered, whose variation does not seem to be correlated with the charge-to-mass ratio, contrary to the situation in Einstein-Maxwell theory.

hep-th↗
arXiv2019

(Generalized) quasi-topological gravities at all orders

A new class of higher-curvature modifications of $D(\geq 4$)-dimensional Einstein gravity has been recently identified. Densities belonging to this "Generalized quasi-topological" class (GQTGs) are characterized by possessing non-hairy generalizations of the Schwarzschild black hole satisfying $g_{tt}g_{rr}=-1$ and by having second-order equations of motion when linearized around maximally symmetric backgrounds. GQTGs for which the equation of the metric function $f(r)\equiv -g_{tt}$ is algebraic are called "Quasi-topological" and only exist for $D\geq 5$. In this paper we prove that GQTG and Quasi-topological densities exist in general dimensions and at arbitrarily high curvature orders. We present recursive formulas which allow for the systematic construction of $n$-th order densities of both types from lower order ones, as well as explicit expressions valid at any order. We also obtain the equation satisfied by $f(r)$ for general $D$ and $n$. Our results here tie up the remaining loose end in the proof presented in arXiv:1906.00987 that every gravitational effective action constructed from arbitrary contractions of the metric and the Riemann tensor is equivalent, through a metric redefinition, to some GQTG.

hep-th↗
arXiv2019

The small black hole illusion

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.

hep-th↗
arXiv2019

Universality of squashed-sphere partition functions

We present several results concerning the free energy of odd-dimensional conformal field theories (CFTs) on squashed spheres. First, we propose a formula which computes this quantity for holographic CFTs dual to higher-curvature gravities with second-order linearized equations of motion. As opposed to standard on-shell action methods for Taub geometries, our formula is automatically UV-finite and only involves a simple evaluation of the corresponding bulk Lagrangian on an auxiliary pure-AdS space. The expression is closely related to the function determining the possible AdS vacua of the bulk theory in question, which we argue to act as a generating functional from which correlation functions of the boundary stress tensor can be easily characterized. Finally, based on holographic results and free-field numerical calculations, we conjecture that the subleading term in the squashing-parameter free-energy expansion is universally controlled by the stress-tensor three-point function charge $t_4$ for general $(2+1)$-dimensional CFTs.

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arXiv2018

Geometric Inflation

We argue that the presence of an inflationary epoch is a natural, almost unavoidable, consequence of the existence of a sensible effective action involving an infinite tower of higher-curvature corrections to the Einstein-Hilbert action. No additional fields besides the metric are required. We show that a family of such corrections giving rise to a well-posed cosmological evolution exists and automatically replaces the radiation-dominated early-universe Big Bang by a singularity-free period of exponential growth of the scale factor, which is gracefully connected with standard late-time $Λ$CDM cosmology. The class of higher-curvature theories giving rise to sensible cosmological evolution share additional remarkable properties such as the existence of Schwarzschild-like non-hairy black holes, or the fact that, just like for Einstein gravity, the only degrees of freedom propagated on the vacuum are those of the standard graviton.

hep-th↗
arXiv2018

Lovelock action with nonsmooth boundaries

We examine the variational problem in Lovelock gravity when the boundary contains timelike and spacelike segments nonsmoothly glued. We show that two kinds of contributions have to be added to the action. The first one is associated to the presence of a boundary in every segment and it depends on intrinsic and extrinsic curvatures. We can think of this contribution as adding a total derivative to the usual surface term of Lovelock gravity. The second one appears in every joint between two segments and it involves the integral along the joint of the Jacobson-Myers entropy density weighted by the Lorentz boost parameter which relates the orthonormal frames in each segment. We argue that this term can be straightforwardly extended to the case of joints involving null boundaries. As an application, we compute the contribution of these terms to the complexity of global AdS in Lovelock gravity by using the "complexity = action" proposal and we identify possible universal terms for arbitrary values of the Lovelock couplings. We find that they depend on the charge $a^*$ controlling the holographic entanglement entropy and on a new constant that we characterize.

gr-qc↗
arXiv2018

NUTs and bolts beyond Lovelock

We construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of several four- and six-dimensional higher-curvature theories of gravity with various base spaces $\mathcal{B}$. In $D=4$, we consider Einsteinian cubic gravity, for which we construct solutions with $\mathcal{B}=\mathbb{S}^2,\mathbb{T}^2$. These represent the first generalizations of the Einstein gravity Taub-NUT/bolt solutions for any higher-curvature theory in four dimensions. In $D=6$, we show that no new solutions are allowed for any Generalized quasi-topological gravity at cubic order. They exist however when we consider quartic Quasi-topological and Generalized quasi-topological terms, for which we construct new solutions with $\mathcal{B}=\mathbb{CP}^2,\mathbb{S}^2\times\mathbb{S}^2,\mathbb{S}^2\times\mathbb{T}^2,\mathbb{T}^2\times\mathbb{T}^2$. In all cases, the solutions are characterized by a single metric function, and they reduce to the corresponding ones in Einstein gravity when the higher-curvature couplings are set to zero. While the explicit profiles must be constructed numerically (except for a few cases), we obtain fully analytic expressions for the thermodynamic properties of all solutions. The new solutions present important differences with respect to Einstein gravity, including regular bolts for arbitrary values of the NUT charge, critical points, and re-entrant phase transitions.

hep-th↗
arXiv2018

Beyond the near-horizon limit: Stringy corrections to Heterotic Black Holes

We study the first-order in $α'$ corrections to 4-charge black holes (with the Reissner-Nordström 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.

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arXiv2018

Regular Stringy Black Holes?

We study the first-order $α'$ 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 $α'$ 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.

hep-th↗
arXiv2018

Holographic studies of Einsteinian cubic gravity

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 Rényi entropies for disk regions on universal quantities characterizing the CFT. In addition, we show that $η/s$ 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.

hep-th↗
arXiv2018

$α'$-corrected black holes in String Theory

We consider the well-known solution of the Heterotic Superstring effective action to zeroth order in $α'$ that describes the intersection of a fundamental string with momentum and a solitonic 5-brane and which gives a 3-charge, static, extremal, supersymmetric black hole in 5 dimensions upon dimensional reduction on $\mathrm{T}^{5}$. We compute explicitly the first-order in $α'$ corrections to this solution, including $\mathrm{SU}(2)$ Yang-Mills fields which can be used to cancel some of these corrections and we study the main properties of this $α'$-corrected solution: supersymmetry, values of the near-horizon and asymptotic charges, behavior under $α'$-corrected T-duality, value of the entropy (using Wald formula directly in 10 dimensions), existence of small black holes etc. The value obtained for the entropy agrees, within the limits of approximation, with that obtained by microscopic methods. The $α'$ corrections coming from Wald's formula prove crucial for this result.

hep-th↗
arXiv2018

Complexity Growth Rate in Lovelock Gravity

Using the "Complexity = Action" framework we compute the late time growth of complexity for charged black holes in Lovelock gravity. Our calculation is facilitated by the fact that the null boundaries of the Wheeler-DeWitt patch do not contribute at late times and essential contributions coming from the joints are now understood arXiv:1803.00172. The late time growth rate reduces to a difference of internal energies associated with the inner and outer horizons, and in the limit where the mass is much larger than the charge, we reproduce the celebrated result of $2M/π$ with corrections proportional to the highest Lovelock coupling in even (boundary) dimensions. We find in some cases a minimum mass below which complexity remains effectively constant, even if the black hole contains a non-degenerate horizon.

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