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We propose a simple algorithm to compute the generalized Komar charge of any exactly gauge- and diffeomorphism-invariant theory., Comment: 6 pages

The Cano-Ruip\'erez 4-dimensional string effective action is the simplest consistent truncation of the first-order in $\alpha'$ heterotic string effective action compactified on T$^{6}$. This theory contains, on top of the metric, a dilaton and an axion that couple to the Gauss-Bonnet term and to the Pontrjagin density which suggests a very strong relation between the physical and geometrical properties of its solutions. In this paper we study the thermodynamics of the string black-hole solutions of this theory using Wald's formalism. We construct the on-shell closed generalized Komar, dilaton and axion 2-form charges, and we used them to find the Smarr formula (that we test on the Schwarzschild and Kerr solutions) and to prove no-(primary)-hair theorems for the scalar. We find that $\alpha'$ plays the role of a thermodynamical variable with an associated chemical potential. We also notice the occurrence of non-standard gravitational charges in the Wald entropy and scalar charges., Comment: 23 pages + appendices

The supersymmetry properties of Killing vectors and spinors in supergravity theory can be clarified by relating them to Killing supervectors in the supergravity superspace. In the superspace approach it is manifest that supersymmetry 'mixes' a Killing vector with its fermionic spinor 'superpartner' and the Killing equations with the generalization of the Killing spinor equations. The latter reduces to the standard Killing spinor equation, albeit with a fermionic spinor, when the fermionic fields are set to zero. Using these supersymmetry transformations in the spacetime component approach, we construct a Noether-Wald charge of ${\cal N}=1$, $D=4$ supergravity with fermionic contributions which is diff-, Lorentz- and supersymmetry-invariant (up to a total derivative). The Killing supervector formalism for the maximal $D=11$ supergravity and some related issues are also discussed., Comment: 12+ pages. IOP conference style. To appear at IOP Conference Proceedings (ISQS28, Prague, Czech Republic)

The standard Komar charge is a $(d-2)$-form that can be defined in spacetimes admitting a Killing vector and which is closed when the vacuum Einstein equations are satisfied. Its integral at spatial infinity (the Komar integral) gives the conserved charge associated to the Killing vector, and, due to its on-shell closedness, the same value (expressed in terms of other physical variables) is obtained integrating over the event horizon (if any). This equality is the basis of the Smarr formula. This charge can be generalized so that it still is closed on-shell in presence of matter and its integrals give generalizations of the Smarr formula. We show how the Komar charge and other closed $(d-2)$-form charges can be used to prove non-existence theorems for gravitational solitons and boson stars. In particular, we show how one can deal with generalized symmetric fields (invariant under a combination of isometries and other global symmetries) and how the geralized symmetric ansatz permits to evade the non-existence theorems., Comment: References added

We study the interactions and the conditions for the equilibrium of forces between generic non-rotating black holes of the Einstein-Maxwell-Dilaton (EMD) theory. We study known (and some new) solutions of the time-symmetric initial-data problem escribing an arbitrary number of those black holes, some of them with primary scalar hair. We show how one can distinguish between initial data corresponding to dynamical situations in which the black holes (one or many) are not in equilibrium and initial data which are just constant-time slices of a static solution of the full equations of motion describing static black holes using (self-)interaction energies. For a single black hole, non-vanishing self-interaction energy is always related to primary scalar hair and to a dynamical black hole. Removing the self-interaction energies in multi-center solutions we get interaction energies related to the attractive and repulsive forces acting on the black holes. As shown by Brill and Lindquist, for widely separated black holes, these take the standard Newtonian and Coulombian forms plus an additional interaction term associated with the scalar charges which is attractive for like charges., Comment: Latex2e file, 38 pages, no figures

We show that, in presence of isometries and non-trivial topology, the Einstein--Hilbert action is invariant under certain transformations of the metric which are not diffeomorphisms. These transformations are similar to the higher-form symmetries of field theories with $p$-form fields. In the context of toroidal Kaluza--Klein compactifications, we show that these symmetries give rise to some of the ``hidden symmetries'' (dualities) of the dimensionally-reduced theories., Comment: LaTeX 2e file, 20 pages, no figures

The dualization of the scalar fields of a theory into (d-2)-form potentials preserving all the global symmetries is one of the main problems in the construction of democratic pseudoactions containing simultaneously all the original fields and their duals. We study this problem starting with the simplest cases and we show how it can be solved for scalars parametrizing Riemannian symmetric sigma-models as in maximal and half-maximal supergravities. Then, we use this result to write democratic pseudoactions for theories in which the scalars are non-minimally coupled to (p+1)-form potentials in any dimension. These results include a proposal of democratic pseudoaction for the generic bosonic sector of 4-dimensional maximal and half-maximal ungauged supergravities. Furthermore, we propose a democratic pseudoaction for the bosonic sector of N=2B,d=10 supergravity (the effective action of the type IIB superstring theory) containing two 0-, two 2-, one 4-, two 6- and three 8-forms which is manifestly invariant under global SL(2,R) transformations., Comment: Misprints corrected in text and some equations. Main results unchanged. Version accepted for publication in SciPost

We consider spacetime metrics with a given (but quite generic) dependence on a dimensionful parameter such that in the 0 and infinity limits of that parameter the metric becomes singular. We study the isometry groups of the original spacetime metrics and of the singular metrics that arise in the limits and the corresponding symmetries of the motion of p-branes evolving in them, showing how the Killing vectors and their Lie algebras can be found in general. We illustrate our general results with several examples which include limits of anti-de Sitter spacetime in which the holographic screen is one of the singular metrics and of pp-waves., Comment: Latex2e paper, 48 pages

We explore the use of the recently defined scalar charge which satisfies a Gauss law in stationary spacetimes, in the context of theories with a scalar potential. We find new conditions that this potential has to satisfy in order to allow for static, asymptotically-flat black-hole solutions with regular horizons and non-trivial scalar field. These conditions are equivalent to some of the known ``no-hair'' theorems (such as Bekenstein's). We study the extended thermodynamics of these systems, deriving a first law and a Smarr formula. As an example, we study the Anabal\'on-Oliva hairy black hole, Comment: author name corrected

Motivated by the current research of generalized symmetries and the construction of conserved charges in pure Einstein gravity linearized over Minkowski spacetime in Cartesian coordinates, we investigate, from a purely classical point of view, the construction of these charges in a coordinate- and frame-independent language in order to generalize them further. We show that all the charges constructed in that context are associated to the conformal Killing-Yano 2-forms of Minkowski spacetime. Furthermore, we prove that those associated to closed conformal Killing-Yano 2-forms are identical to the charges constructed by Kastor and Traschen for their dual Killing-Yano (d-2)-forms. We discuss the number of independent and non-trivial gravitational charges that can be constructed in this way., Comment: References added and some typos corrected. Version to be published in JHEP

We study the invariance of N=1,d=4 supergravity solutions under diffeormophisms and show that, in order to obtain consistent conditions (``Killing equations'') invariant under local supersymmetry transformations, one has to perform supersymmetry transformations generated by the superpartner of the vector that generates standard diffeomorphisms, just as a superspace analysis indicates. Using these transformations, we construct a Noether-Wald charge of N=1,d=4 supergravity with fermionic contributions which is diff- Lorentz- and supersymmetry-invariant (up to a total derivative)., Comment: Title changed to represent betterthe content. References added

We study the thermodynamics of the 4-dimensional electrically charged black-hole solutions of the simplest 5-dimensional Kaluza-Klein theory using Wald's formalism. We show how the electric work term present in the 4-dimensional first law of black-hole thermodynamics arises in the purely gravitational 5-dimensional framework. In particular, we find an interesting geometric interpretation of the 4-dimensional electrostatic potential similar to the angular velocity in rotating black holes. Furthermore, we show how the momentum map equation arises from demanding compatibility between the timelike Killing vector of the black-hole solution and the spatial Killing vector of the 5-dimensional background., Comment: LaTeX2e file, 34 pages, no figures

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar and Abelian vector fields coupled to gravity using Wald's formalism and a new definition of scalar charge as an integral over a 2-surface which satisfies a Gauss law in stationary black-hole spacetimes. We focus on ungauged supergravity-inspired theories with symmetric sigma models whose symmetries generate electric-magnetic dualities leaving invariant their equations of motion. Our manifestly duality-invariant form of the first law is compatible with the one obtained by of Gibbons, Kallosh and Kol. We also obtain the general expression for the scalar charges of a stationary black hole in terms of the other physical parameters of the solution and the position of the horizon, generalizing the expression obtained by Pacilio for dilaton black oles., Comment: Misprints corrected and a few comments and references added. Version to be published in JHEP

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

Using Wald's formalism, we study the thermodynamics (first laws and Smarr formulae) of asymptotically-flat black holes, rings etc. in a higher-dimensional higher-rank generalization of the Einstein-Maxwell theory. We show how to deal with the electric and magnetic charges of the objects and how the electric-magnetic duality properties of the theory are realized in the first laws and Smarr formulae., Comment: Latex 2e file, 24 pages, no figures Some references added and some typos corrected. Version to be published in JHEP

We study black-hole thermodynamics in theories that contain dimensionful constants such as the cosmological constant or coupling constants in Wald's formalism. The most natural way to deal with these constants is to promote them to scalar fields introducing a (d-1)-form Lagrange multiplier that forces them to be constant on-shell. These (d-1)-form potentials provide a dual description of them and, in the context of superstring/supergravity theories, a higher-dimensional origin/explanation. In the context of gauged supergravity theories, all these constants can be collected in the embedding tensor. We show in an explicit 4-dimensional example that the embedding tensor can also be understood as a thermodynamical variable that occurs in the Smarr formula in a duality-invariant fashion. This establishes an interesting link between black-hole thermodynamics, gaugings and compactifications in the context of superstring/supergravity theories., Comment: References added, 43 pages, no figures

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 construct the Komar integral for axion-dilaton gravity using Wald's formalism and momentum maps and we use it to derive a Smarr relation for stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is not invariant under SL(2,R) electric-magnetic duality transformations because Wald's formalism does not account for magnetic charges and potentials, the Komar integral constructed with it turns out to be invariant and, in more general theories, it will be fully symplectic invariant. We check the Smarr formula obtained with the most general family of static axion-dilaton black holes., Comment: LaTeX file, 19 pages, no figures

We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in alpha prime using Wald's formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in alpha prime that can be reliably used in a comparison with the microscopic ones. Such a formula was still lacking in the literature. In the proof we use momentum maps to define covariant variations and Lie derivatives and \textit{restricted generalized zeroth laws} which state the closedness of certain differential forms on the bifurcation sphere and imply the constancy of the associated potentials on it. We study the relation between our entropy formula and other formulae that have been used in the literature., Comment: 35 pages, no figures

We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in alpha prime, using Wald's formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. This work is a first step towards the derivation of the first law at first order in alpha prime where, more complicated, non-Abelian, Lorentz ("gravitational") and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies., Comment: A complete example in which the momentum maps of a non-extremal, charged, black ring are computed, has been added to the paper. 45 pages

We re-derive the first law of black hole mechanics in the context of the Einstein-Maxwell theory in a gauge-invariant way introducing "momentum maps" associated to field strengths and the vectors that generate their symmetries. These objects play the role of generalized thermodynamical potentials in the first law and satisfy generalized zeroth laws, as first observed in the context of principal gauge bundles by Prabhu, but they can be generalized to more complex situations. We test our ideas on the $d$-dimensional Reissner-Nordstr\"om-Tangherlini black hole., Comment: Some references added

We perform the toroidal compactification of the full Bergshoeff-de Roo version of the Heterotic Superstring effective action to first orderin $\alpha'$. The dimensionally-reduced action is given in a manifestly-O(n,n)-invariant form which we use to derive a manifestly-O(n,n)-invariant Wald entropy formula which we then use to compute the entropy of $\alpha'$-corrected, 4-dimensional, 4-charge, static, extremal, supersymmetric black holes., Comment: References and comments added. Version to be published in Journal of High Energy Physics

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter $\alpha'$ and re-derive the $\alpha'$-corrected Buscher rules first found in arXiv:hep-th/9506156 , proving the T duality invariance of the dimensionally-reduced action to that order in $\alpha'$. We use Iyer and Wald's prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the $\alpha'$-corrected T duality transformations. This formula has been successfully applied to $\alpha'$-corrected 4-dimensional non-extremal Reissner-Nordstr\"om black holes in arXiv:1910.14324 and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole., Comment: Misprints in intermediate equations corrected in agreement with the erratum submitted to the journal. Final results not affected

We study the first-order in $\alpha'$ corrections to non-extremal 4-dimensional dyonic Reissner-Nordstr\"om (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 $\alpha'$, 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., Comment: 22 pages + appendices, 2 figures

We consider the effective action of the Heterotic Superstring to first order in alpha prime and derive the necessary and sufficient conditions that a field configuration has to satisfy in order to admit at least one Killing spinor using the spinor bilinear method and making minimal coordinate and frame choices. As a previous step in this derivation, we compute the complete spinor bilinear algebra using the Fierz identities, obtaining as a by-product the algebra satisfied by the Spin(7) structure contained in the bilinears in an arbitrary basis. We find the relations existing between the left-hand-sides of the bosonic equations of motion evaluated on supersymmetric field configurations using the Killing Spinor Identities instead of the (far more complicated) integrability conditions of the Killing Spinor Equations as it is common in the literature. We show how to include the Kalb-Ramond's Bianchi identity in the Killing Spinor Identities., Comment: LaTeX2e file, 49 pages, no figures. An error in the derivation of necessary conditions for unbroken supersymmetry and a few typos have been corrected

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., Comment: 22 pages

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 show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its applications by giving several explicit examples. The method can be generalized to include the construction of actions for ultra-relativistic gravity, i.e. Carroll gravity, and non-relativistic supergravity as well., Comment: 37 pages, 1 figure; v2: minor editing plus added references

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 characterize all the supersymmetric configurations and solutions of minimal N=(1,0), d=6 supergravity coupled in the most general gauge-invariant way to an arbitrary number of tensor and vector multiplets and hypermultiplets., Comment: Title changed and comments added. Version published in CQG

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 consider the well-known solution of the Heterotic Superstring effective action to zeroth order in $\alpha'$ 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 $\alpha'$ 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 $\alpha'$-corrected solution: supersymmetry, values of the near-horizon and asymptotic charges, behavior under $\alpha'$-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 $\alpha'$ corrections coming from Wald's formula prove crucial for this result., Comment: 40 pages, 1 figure; Reference added, typos corrected

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.

We construct a solution of Heterotic supergravity which interpolates between two different AdS$_{3}\times S^{3}\times T^{4}$ geometries corresponding to the near-horizon limits of two 5-dimensional black holes, only one of which has non-Abelian hair. This solution can be used to estimate the amplitude of probability of the non-perturbative decay of the gauge 5-brane responsible for the non-Abelian hair into eight solitonic 5-branes by evaluating its Euclidean action. The Wick rotation of this solution poses several problems which we argue can be overcome by using a non-extremal off-shell (NEOS) deformation of the solution. This NEOS field configuration can be Wick rotated straight away and its Euclidean action can be computed for any value of the deformation parameter. The Euclidean result can then be anti-Wick-rotated and its extremal limit gives the Euclidean action of the original solution, which turns out to be one half of the difference between the entropies of the 5-dimensional black holes., Comment: Few typos corrected. Two references and a footnote added. Version to be published in JHEP

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 show that, in all metric theories of gravity with a general covariant action, gravity couples to the gravitational energy-momentum tensor in the same way it couples to the matter energy-momentum tensor order by order in the weak field approximation around flat spacetime. We discuss the relation of this property to the Strong Equivalence Principle. We also study the gauge transformation properties of the gravitational energy-momentum tensor., Comment: Additional resulting the gauge transformation of the gravitational energy-momentum tensor and references added. 18 pages, no figures

We study a family of 5-dimensional non-Abelian black holes that can be obtained by adding an instanton field to the well-known D1D5W Abelian black holes. Naively, the non-Abelian fields seem to contribute to the black-hole entropy but not to the mass due to their rapid fall-off at spatial infinity. By uplifting the 5-dimensional supergravity solution to 10-dimensional Heterotic Supergravity first and then dualizing it into a Type-I Supergravity solution, we show that the non-Abelian fields are associated to D5-branes dissolved into the D9-branes (dual to the Heterotic "gauge 5-branes") and that their associated RR charge does not, in fact, contribute to the entropy, which only depends on the number16 pages of D-strings and D5 branes and the momentum along the D-strings, as in the Abelian case. These "dissolved" or "gauge" D5-branes do contribute to the mass in the expected form. The correct interpretation of the 5-dimensional charges in terms of the string-theory objects solves the non-Abelian hair puzzle, allowing for the microscopic accounting of the entropy. We discuss the validity of the solution when alpha prime corrections are taken into account., Comment: Latex 2e file, 21 pages. A full appendix on alpha prime corrections and the corresponding discussions have been added. The conclusions have suffered minor changes. Version accepted in JHEP

We present an asymptotically flat, spherically symmetric, static, globally regular and horizonless solution of SU$(2)$-gauged $\mathcal{N}=1,d=5$ supergravity. The SU$(2)$ gauge field is that of the BPST instanton. We argue that this solution, analogous to the global monopoles found in $d=4$ $\mathcal{N}=2$ and $\mathcal{N}=4$ gauged supergravities, describes the field of a single string-theory object which does not contribute to the entropy of black holes when we add it to them and show that it is, indeed, the dimensional reduction on T$^{5}$ of the gauge 5-brane. We investigate how the energy of the solution is concentrated as a function of the instanton's scale showing that it never violates the hoop conjecture although the curvature grows unboundedly in the zero scale limit., Comment: 19 pages, 4 figures. Some misprints corrected

We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the K\"ahler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple second-order differential equation. Using this general form of the base space, the equations satisfied by the building blocks of the solutions become of, at most, fourth degree and can be solved by simple polynomic ansatzs. In this way we construct two 3-parameter families of solutions that contain almost all the timelike supersymmetric solutions of this theory with one angular momentum known so far and a few more: the (singular) supersymmetric Reissner-Nordstr\"om-AdS solutions, the three exact supersymmetric solutions describing the three near-horizon geometries found by Gutowski and Reall, three 1-parameter asymptotically-AdS$_{5}$ black-hole solutions with those three near-horizon geometries (Gutowski and Reall's black hole being one of them), three generalizations of the G\"odel universe and a few potentially homogenous solutions. A key r\^ole in finding these solutions is played by our ability to write AdS$_{5}$'s K\"ahler base space ($\overline{\mathbb{CP}}^{2}$ or SU$(1,2)/$U$(2)$) is three different, yet simple, forms associated to three different isometries. Furthermore, our ansatz for the K\"ahler metric also allows us to study the dimensional compactification of the theory and its solutions in a systematic way., Comment: 57 pages. References and comments added

We show how to write any Kaehler metric of complex dimension 2 admitting a holomorphic isometry as a simple 1-real-function deformation of a Gibbons-Hawking metric. Hyper-Kaehler metrics with a tri-holomorphic isometry (Gibbons-Hawking metrics) or with a mono-holomorphic isometry are recovered for particular values of the additional function. The new general metric can be used as an Ansatz in several interesting physical problems., Comment: Two references added. A very important comment concerning the novelty of the results presented has also been added in the front page

We explore the construction of supersymmetric solutions of theories of N=2,d=4 supergravity with a SU(2) gauging and SU(2) Fayet-Iliopoulos terms. In these theories an SU(2) isometry subgroup of the Special Kahler manifold is gauged together with a SU(2) R-symmetry subgroup. We construct several solutions of the CP3 quadratic model directly in four dimensions and of the ST[2,6] model by dimensional reduction of the solutions found by Cariglia and Mac Conamhna in N=(1,0),d=6 supergravity with the same kind of gauging. In the CP3 model, we construct an AdS2xS2 solution which is only 1/8 BPS and an RxH3 solution that also preserves 1 of the 8 possible supersymmetries. We show how to use dimensional reduction as in the ungauged case to obtain RnxSm and also AdSnxSm-type solutions (with different radii) in - and 4 dimensions from the 6-dimensional AdS3xS3 solution., Comment: Latex 2e file, 37 pages, 1 figure. A paragraph on Fayet-Iliopoulos gaugings rewritten and minor typos corrected. Version to be published in Nuclear Physics B

We show that, when compactified on a circle, N=(2,0),d=6 supergravity coupled to 1 tensor multiplet and nV vector multiplets is dual to N=(2,0),d=6 supergravity coupled to just nT=nV+1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N=2,d=5 supergravity coupled to nV5=nV+2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N=2,d=5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions. One of the solutions obtained interpolates smoothly between two AdS3xS3 geometries with different radii., Comment: A few typos corrected in text and formulae. Version to be published in JHEP

We study the gauging of maximal $d=8$ supergravity using the embedding tensor formalism. We focus on SO$(3)$ gaugings, study all the possible choices of gauge fields and construct explicitly the bosonic actions (including the complicated Chern-Simons terms) for all these choices, which are parametrized by a parameter associated to the 8-dimensional SL$(2,\mathbb{R})$ duality group that relates all the possible choices which are, ultimately, equivalent from the purely 8-dimensional point of view. Our result proves that the theory constructed by Salam and Sezgin by Scherk-Schwarz compactification of $d=11$ supergravity and the theory constructed in Ref.~\cite{AlonsoAlberca:2000gh} by dimensional reduction of the so called ``massive 11-dimensional supergravity'' proposed by Meessen and Ort\'{\i}n in Ref.~\cite{Meessen:1998qm} are indeed related by an SL$(2,\mathbb{R})$ duality even though they have two completely different 11-dimensional origins., Comment: 28 pages

We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them., Comment: 39 pages

We review and investigate different aspects of scalar fields in supergravity theories both when they parametrize symmetric spaces and when they parametrize spaces of special holonomy which are not necessarily symmetric (Kahler and Quaternionic-Kahler spaces): their role in the definition of derivatives of the fermions covariant under the R-symmetry group and (in gauged supergravities) under some gauge group, their dualization into (d-2)-forms, their role in the supersymmetry transformation rules (via fermion shifts, for instance) etc. We find a general definition of momentum map that applies to any manifold admitting a Killing vector and coincides with those of the holomorphic and tri-holomorphic momentum maps in Kahler and Quaternionic-Kahler spaces and with an independent definition that can be given in symmetric spaces. We show how the momentum map occurs ubiquitously: in gauge-covariant derivatives of fermions, in fermion shifts, in the supersymmetry transformation rules of (d-2)-forms etc. We also give the general structure of the Noether-Gaillard-Zumino conserved currents in theories with fields of different ranks in any dimension., Comment: 62 pages. A few minor misprints corrected

We construct a supersymmetric black ring solution of SU(2) N=1, d=5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric coloured black holes recently constructed in the same theory and in N=2, d=4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution., Comment: 19 pages, no figures

We construct and study the first supersymmetric black-hole and black-string solutions of non-Abelian-gauged N=1,d=5 supergravity (N=1,d=5 Super-Einstein-Yang-Mills theory) with non-trivial SU(2) gauge fields: BPST instantons for black holes and BPS monopoles of different kinds ('t~Hooft-Polyakov, Wu-Yang and Protogenov) for black strings and also for certain black holes that are well defined solutions only for very specific values of all the moduli. Instantons, as well as colored monopoles do not contribute to the masses and tensions but do contribute to the entropies. The construction is based on the characterization of the supersymmetric solutions of gauged N=1,d=5 supergravity coupled to vector multiplets achieved in Ref. Bellorin:2007yp which we elaborate upon by finding the rules to construct supersymmetric solutions with one additional isometry, both for the timelike and null classes. These rules automatically connect the timelike and null non-Abelian supersymmetric solutions of N=1,d=5 SEYM theory with the timelike ones of N=2,d=4 SEYM theory by dimensional reduction and oxidation. In the timelike-to-timelike case the singular Kronheimer reduction recently studied in Ref. Bueno:2015wva plays a crucial role., Comment: 37 pages, no figures