arXiv subjects

Ángel Murcia

Publications and source records attributed to Ángel Murcia.

15 recordsLinked to original sources

arXiv2024

Supersymmetric Kundt four manifolds and their spinorial evolution flows

We investigate the differential geometry and topology of four-dimensional Lorentzian manifolds $(M,g)$ equipped with a real Killing spinor $\varepsilon$, where $\varepsilon$ is defined as a section of a bundle of irreducible real Clifford modules satisfying the Killing spinor equation with non-zero real constant. Such triples $(M,g,\varepsilon)$ are precisely the supersymmetric configurations of minimal four-dimensional supergravity and necessarily belong to the class Kundt of space-times, hence we refer to them as supersymmetric Kundt configurations. We characterize a class of Lorentzian metrics on $\mathbb{R}^2\times X$, where $X$ is a two-dimensional oriented manifold, to which every supersymmetric Kundt configuration is locally isometric, proving that $X$ must be an elementary hyperbolic Riemann surface when equipped with the natural induced metric. This yields a class of space-times that vastly generalize the Siklos class of space-times describing gravitational waves in AdS$_4$. Furthermore, we study the Cauchy problem posed by a real Killing spinor and we prove that the corresponding evolution problem is equivalent to a system of differential flow equations, the real Killing spinorial flow equations, for a family of functions and coframes on any Cauchy hypersurface $Σ\subset M$. Using this formulation, we prove that the evolution flow defined by a real Killing spinor preserves the Hamiltonian and momentum constraints of the Einstein equation with negative curvature and is therefore compatible with the latter. Moreover, we explicitly construct all left-invariant evolution flows defined by a Killing spinor on a simply connected three-dimensional Lie group, classifying along the way all solutions to the corresponding constraint equations, some of which also satisfy the constraint equations associated to the Einstein condition.

math.DG↗

arXiv2023

Parallel spinor flows on three-dimensional Cauchy hypersurfaces

The three-dimensional parallel spinor flow is the evolution flow defined by a parallel spinor on a globally hyperbolic Lorentzian four-manifold. We prove that, despite the fact that Lorentzian metrics admitting parallel spinors are not necessarily Ricci flat, the parallel spinor flow preserves the vacuum momentum and Hamiltonian constraints and therefore the Einstein and parallel spinor flows coincide on common initial data. Using this result, we provide an initial data characterization of parallel spinors on Ricci flat Lorentzian four-manifolds, which in turn yields the first initial data characterization of Ricci-flat pp-waves. Furthermore, we explicitly solve the left-invariant parallel spinor flow on simply connected Lie groups, obtaining along the way necessary and sufficient conditions for the flow to be immortal. These are, to the best of our knowledge, the first non-trivial examples of evolution flows of parallel spinors. Finally, we use some of these examples to construct families of $η\,$-Einstein cosymplectic structures and to produce solutions to the left-invariant Ricci flow in three dimensions. This suggests the intriguing possibility of using first-order hyperbolic spinorial flows to construct special solutions of curvature flows in Riemannian signature.

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arXiv2023

Heterotic solitons on four-manifolds

We investigate four-dimensional Heterotic solitons, defined as a particular class of solutions of the equations of motion of Heterotic supergravity on a four-manifold $M$. Heterotic solitons depend on a parameter $κ$ and consist of a Riemannian metric $g$, a metric connection with skew torsion $H$ on $TM$ and a closed one-form $φ$ on $M$ satisfying a differential system. In the limit $κ\to 0$, Heterotic solitons reduce to a class of generalized Ricci solitons and can be considered as a higher-order curvature modification of the latter. If the torsion $H$ is equal to the Hodge dual of $φ$, Heterotic solitons consist of either flat tori or closed Einstein-Weyl structures on manifolds of type $S^1\times S^3$ as introduced by P. Gauduchon. We prove that the moduli space of such closed Einstein-Weyl structures is isomorphic to the product of $\mathbb{R}$ with a certain finite quotient of the Cartan torus of the isometry group of the typical fiber of a natural fibration $M\to S^1$. We also consider the associated space of essential infinitesimal deformations, which we prove to be obstructed. More generally, we characterize several families of Heterotic solitons as suspensions of certain three-manifolds with prescribed constant principal Ricci curvatures, amongst which we find hyperbolic manifolds, manifolds covered by $\widetilde{\mathrm{Sl}}(2,\mathbb{R})$ and E$(1,1)$ or certain Sasakian three-manifolds. These solutions exhibit a topological dependence in the string slope parameter $κ$ and yield, to the best of our knowledge, the first examples of Heterotic compactification backgrounds not locally isomorphic to supersymmetric compactification backgrounds.

math.DG↗

arXiv2022

$\varepsilon\,$-contact structures and six-dimensional supergravity

We introduce the concept of $\varepsilon\,$-contact metric structures on oriented (pseudo-)Riemannian three-manifolds, which encompasses the usual Riemannian contact metric, Lorentzian contact metric and para-contact metric structures, but which also allows the possibility for the Reeb vector field to be null. We investigate in more detail this latter case, which we call null contact structure. We observe that it is possible to extend in a natural and meaningful way both the Sasaki and K-contact conditions for null-contact structures, but we find that they are not equivalent conditions, in contradistinction to the situation for non-lightlike Reeb vector fields. Finally, we define the notion of $\varepsilonη\,$-Einstein structures and we discover that appropriate direct products of these structures produce solutions of six-dimensional minimal supergravity coupled to a tensor multiplet with constant dilaton.

math.DG↗

arXiv2022

Higher-derivative holography with a chemical potential

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the $d$-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified $\langle JJ\rangle$ correlator as well as to a general $\langle TJJ \rangle$ structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of $\langle JJ\rangle$ and $\langle TJJ \rangle$.

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arXiv2022

A universal feature of charged entanglement entropy

Rényi entropies, $S_n$, admit a natural generalization in the presence of global symmetries. These "charged Rényi entropies" are functions of the chemical potential $μ$ conjugate to the charge contained in the entangling region and reduce to the usual notions as $μ\rightarrow 0$. For $n=1$, this provides a notion of charged entanglement entropy. In this letter we prove that for a general $d (\geq 3)$-dimensional CFT, the leading correction to the uncharged entanglement entropy across a spherical entangling surface is quadratic in the chemical potential, positive definite, and universally controlled (up to fixed $d$-dependent constants) by the coefficients $C_J$ and $a_2$. These fully characterize, for a given theory, the current correlators $\langle JJ\rangle $ and $\langle TJJ \rangle$, as well as the energy flux measured at infinity produced by the insertion of the current operator. Our result is motivated by analytic holographic calculations for a special class of higher-curvature gravities coupled to a $(d-2)$-form in general dimensions as well as for free-fields in $d=4$. A proof for general theories and dimensions follows from previously known universal identities involving the magnetic response of twist operators introduced in arXiv:1310.4180 and basic thermodynamic relations.

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arXiv2021

Parallel spinors on globally hyperbolic Lorentzian four-manifolds

We investigate the differential geometry and topology of globally hyperbolic four-manifolds $(M,g)$ admitting a parallel real spinor $\varepsilon$. Using the theory of parabolic pairs recently introduced in arXiv:1911.08658 , we first formulate the parallelicity condition of $\varepsilon$ on $M$ as a system of partial differential equations, the parallel spinor flow equations, for a family of polyforms on any given Cauchy surface $Σ\hookrightarrow M$. Existence of a parallel spinor on $(M,g)$ induces a system of constraint partial differential equations on $Σ$, which we prove to be equivalent to an exterior differential system involving a cohomological condition on the shape operator of the embedding $Σ\hookrightarrow M$. Solutions of this differential system are precisely the allowed initial data for the evolution problem of a parallel spinor and define the notion of parallel Cauchy pair $(\mathfrak{e},Θ)$, where $\mathfrak{e}$ is a coframe and $Θ$ is a symmetric two-tensor. We characterize all parallel Cauchy pairs on simply connected Cauchy surfaces, refining a result of Baum, Leistner and Lischewski. Furthermore, we classify all compact three-manifolds admitting parallel Cauchy pairs, proving that they are canonically equipped with a locally free action of $\mathbb{R}^2$ and are isomorphic to certain torus bundles over $S^1$, whose Riemannian structure we characterize in detail. Moreover, we classify all left-invariant parallel Cauchy pairs on simply connected Lie groups, specifying when they are allowed initial data for the Ricci flat equations and when the shape operator is Codazzi. Finally, we give a novel geometric interpretation of a class of parallel spinor flows and solve it in several examples, obtaining explicit families of four-dimensional Lorentzian manifolds carrying parallel spinors.

math.DG↗

arXiv2021

Heisenberg-invariant self-dual Einstein manifolds

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can take any value. Then we study when the corresponding (Riemannian or neutral-signature) metrics are (geodesically) complete. Finally, we exhibit the solutions of non-zero Ricci-curvature as different branches of one-loop deformed universal hypermultiplets in Riemannian and neutral signature.

math.DG↗

arXiv2021

Exact electromagnetic duality with nonminimal couplings

We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging problem. Despite that, we manage to obtain a closed form of the action for all the theories with a quadratic dependence on the vector field strength. In these theories we find that the Maxwell field couples to gravity through a curvature-dependent susceptibility tensor that takes a peculiar form, reminiscent of that of Born-Infeld Lagrangians. We study the static and spherically symmetric black hole solutions of the simplest of these models, showing that the corresponding equations of motion are invariant under rotations of the electric and magnetic charges. We compute the perturbative corrections to the Reissner-Nordström solution in this theory, and in the case of extremal black holes we determine exactly the near-horizon geometry as well as the entropy. Remarkably, the entropy only possesses a constant correction despite the action containing an infinite number of terms. In addition, we find there is a lower bound for the charge and the mass of extremal black holes. When the sign of the coupling is such that the weak gravity conjecture is satisfied, the area and the entropy of extremal black holes vanish at the minimal charge.

hep-th↗

arXiv2021

On small black holes, KK monopoles and solitonic 5-branes

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.

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arXiv2021

Duality-invariant extensions of Einstein-Maxwell theory

We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e, that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.

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arXiv2021

Electromagnetic Quasitopological Gravities

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function $f(r)=-g_{tt}=1/g_{rr}$. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for $f(r)$. Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.

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arXiv2021

Contact metric three manifolds and Lorentzian geometry with torsion in six-dimensional supergravity

We introduce the notion of $\varepsilonη\,$-Einstein $\varepsilon\,$-contact metric three-manifold, which includes as particular cases $η\,$-Einstein Riemannian and Lorentzian (para) contact metric three-manifolds, but which in addition allows for the Reeb vector field to be null. We prove that the product of an $\varepsilonη\,$-Einstein Lorentzian $\varepsilon\,$-contact metric three-manifold with an $\varepsilonη\,$-Einstein Riemannian contact metric three-manifold carries a bi-parametric family of Ricci-flat Lorentzian metric-compatible connections with isotropic, totally skew-symmetric, closed and co-closed torsion, which in turn yields a bi-parametric family of solutions of six-dimensional minimal supergravity coupled to a tensor multiplet. This result allows for the systematic construction of families of Lorentzian solutions of six-dimensional supergravity from pairs of $\varepsilonη\,$-Einstein contact metric three-manifolds. We classify all left-invariant $\varepsilonη\,$-Einstein structures on simply connected Lie groups, paying special attention to the case in which the Reeb vector field is null. In particular, we show that the Sasaki and K-contact notions extend to $\varepsilon\,$-contact structures with null Reeb vector field but are however not equivalent conditions, in contrast to the situation occurring when the Reeb vector field is not light-like. Furthermore, we pose the Cauchy initial-value problem of an $\varepsilon\,$-contact $\varepsilonη\,$-Einstein structure, briefly studying the associated constraint equations in a particularly simple decoupling limit. Altogether, we use these results to obtain novel families of six-dimensional supergravity solutions, some of which can be interpreted as continuous deformations of the maximally supersymmetric solution on $\widetilde{\mathrm{Sl}}(2,\mathbb{R})\times S^3$.

math.DG↗

arXiv2020

Resolution of Reissner-Nordström singularities by higher-derivative corrections

We describe a non-minimal higher-derivative extension of Einstein-Maxwell theory in which electrically-charged black holes and point charges have globally regular gravitational and electromagnetic fields. We provide an exact static spherically symmetric solution of this theory that reduces to the Reissner-Nordström one at weak coupling, but in which the singularity at $r=0$ is regularized for arbitrary mass and (non-vanishing) charge. We discuss the properties of these solutions and comment on the physical significance of our results.

hep-th↗

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.

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