Tomas Ortin - Academia.edu (original) (raw)

Papers by Tomas Ortin

SciPost Physics Core

We compute the first-order \alpha'α′ corrections to well-known families of heterotic multi-ce... more We compute the first-order \alpha'α′ 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'α′ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation.

Nuclear Physics B, Aug 1, 2006

We classify all the supersymmetric configurations of ungauged N = 2, d = 4 supergravity coupled t... more We classify all the supersymmetric configurations of ungauged N = 2, d = 4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric configurations fall into two classes, depending on the timelike or null nature of the Killing vector constructed from Killing spinor bilinears. The timelike class configurations are essentially the ones found by Behrndt, Lüst and Sabra, which exhaust this class and are the ones that include supersymmetric black holes. The null class configurations include pp-waves and cosmic strings.

arXiv (Cornell University), Feb 22, 2023

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar... more 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 the background of 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 holes. a Email: romina.ballesteros[at]estudiante.uam.es b Email: carmen.gomez-fayren[at]estudiante.uam.es c Email: tomas.ortin[at]csic.es d Email: matteo.zatti[at]estudiante.uam.es

arXiv (Cornell University), Nov 30, 2021

We study extremal 5-and 4-dimensional black hole solutions of the Heterotic Superstring effective... more We study extremal 5-and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in α 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 α corrections are drastically different depending on how we break supersymmetry. We provide fully analytic O(α) solutions and we compute their charges, masses and entropies and check that they are invariant under α-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. a Email: pabloantonio.cano[at]kuleuven.be b Email: tomas.ortin[at]csic.es c Email: alejandro.ruiperez[at]pd.infn.it d Email: matteo.zatti[at]estudiante.uam.es

arXiv (Cornell University), Apr 13, 2018

We characterize all the supersymmetric configurations and solutions of minimal (N = (1, 0)) d = 6... more We characterize all the supersymmetric configurations and solutions of minimal (N = (1, 0)) d = 6 supergravity coupled in the most general gaugeinvariant way to an arbitrary number of tensor and vector multiplets and hypermultiplets.

arXiv (Cornell University), Oct 6, 2016

We show how to write any Kähler metric of complex dimension 2 admitting a holomorphic isometry as... more We show how to write any Kähler metric of complex dimension 2 admitting a holomorphic isometry as a simple 1-real-function deformation of a Gibbons-Hawking metric. Hyper-Kähler 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. 1 Important notice: After the first submission of this paper to the arXiv, we have realized that the main result presented in it was implicitly contained in Ref. [10], as explained in Section 2 of Ref. [15], something neither we nor the experts we consulted before the submission were aware of. While this paper cannot be published in a regular scientific journal, we think it still can be useful for the scientific community. b E-mail: Samuele.Chimento [at] csic.es c E-mail: Tomas.Ortin [at] csic.es

Cambridge University Press eBooks, Apr 7, 2015

arXiv (Cornell University), May 31, 2016

We study the gauging of maximal d = 8 supergravity using the embedding tensor formalism. We focus... more 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, 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. [6] by dimensional reduction of the so called "massive 11-dimensional supergravity" proposed by Meessen and Ortín in Ref. [7] are indeed related by an SL(2, R) duality even though they have two completely different 11-dimensional origins.

arXiv (Cornell University), Dec 25, 2020

We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring ef... more 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 α , 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. We study explicitly a non-extremal, charged, black ring solution of pure N = 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory. This work is a first step towards the derivation of the first law at first order in α 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.

Journal of High Energy Physics

Motivated by the current research of generalized symmetries and the construction of conserved cha... more 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.

AIP Conference Proceedings, 2001

Journal of High Energy Physics, 2017

We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for... more We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the Kähler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple secondorder 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 3parameter 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-Nordström-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 Gödel universe and a few potentially homogenous solutions. A key rôle in finding these solutions is played by our ability to write AdS 5 's Kähler base space (CP 2 or SU(1, 2)/U(2)) is three different, yet simple, forms associated to three different isometries. Furthermore, our ansatz for the Kähler metric also allows us to study the dimensional compactification of the theory and its solutions in a systematic way.

Physics Letters B, 1989

Introducing a geometric normal ordering, we give a proof of BRST invariance of the states associa... more Introducing a geometric normal ordering, we give a proof of BRST invariance of the states associated to an arbitrary genus Riemann surface with a puncture, in the operator formalism. FTUAM/88-35 * Work supported in part by the program 'Ayudas para estancias breves en centros de investigación de España y el extranjero', (Comunidad Autónoma de Madrid).

Journal of High Energy Physics

We study the thermodynamics of the 4-dimensional electrically charged black-hole solutions of the... more 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.

Journal of High Energy Physics

Using Wald’s formalism, we study the thermodynamics (first laws and Smarr formulae) of asymptotic... more 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 their thermodynamics.

Journal of High Energy Physics

We construct the Komar integral for axion-dilaton gravity using Wald’s formalism and momentum map... more 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.

Journal of High Energy Physics, 2021

We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvatur... more We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence betweenf(R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables (pressures) and we give a general expression for their conjugate potentials (volumes).

Journal of High Energy Physics, 2021

A correction to this paper has been published: https://doi.org/10.1007/JHEP06(2020)106

Journal of High Energy Physics, 2021

We prove the first law of black hole mechanics in the context of the Heterotic Superstring effect... more We prove the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in α′, 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. We study explicitly a non-extremal, charged, black ring solution of pure mathcalN\mathcal{N}mathcalN N = 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory.This work is a first step towards the derivation of the first law at first order in α′ where, more complicated, non-Abelian, Lorentz (“gravitational”) and ...

SciPost Physics Core

We compute the first-order \alpha'α′ corrections to well-known families of heterotic multi-ce... more We compute the first-order \alpha'α′ 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'α′ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation.

Nuclear Physics B, Aug 1, 2006

We classify all the supersymmetric configurations of ungauged N = 2, d = 4 supergravity coupled t... more We classify all the supersymmetric configurations of ungauged N = 2, d = 4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric configurations fall into two classes, depending on the timelike or null nature of the Killing vector constructed from Killing spinor bilinears. The timelike class configurations are essentially the ones found by Behrndt, Lüst and Sabra, which exhaust this class and are the ones that include supersymmetric black holes. The null class configurations include pp-waves and cosmic strings.

arXiv (Cornell University), Feb 22, 2023

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar... more 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 the background of 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 holes. a Email: romina.ballesteros[at]estudiante.uam.es b Email: carmen.gomez-fayren[at]estudiante.uam.es c Email: tomas.ortin[at]csic.es d Email: matteo.zatti[at]estudiante.uam.es

arXiv (Cornell University), Nov 30, 2021

We study extremal 5-and 4-dimensional black hole solutions of the Heterotic Superstring effective... more We study extremal 5-and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in α 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 α corrections are drastically different depending on how we break supersymmetry. We provide fully analytic O(α) solutions and we compute their charges, masses and entropies and check that they are invariant under α-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. a Email: pabloantonio.cano[at]kuleuven.be b Email: tomas.ortin[at]csic.es c Email: alejandro.ruiperez[at]pd.infn.it d Email: matteo.zatti[at]estudiante.uam.es

arXiv (Cornell University), Apr 13, 2018

We characterize all the supersymmetric configurations and solutions of minimal (N = (1, 0)) d = 6... more We characterize all the supersymmetric configurations and solutions of minimal (N = (1, 0)) d = 6 supergravity coupled in the most general gaugeinvariant way to an arbitrary number of tensor and vector multiplets and hypermultiplets.

arXiv (Cornell University), Oct 6, 2016

We show how to write any Kähler metric of complex dimension 2 admitting a holomorphic isometry as... more We show how to write any Kähler metric of complex dimension 2 admitting a holomorphic isometry as a simple 1-real-function deformation of a Gibbons-Hawking metric. Hyper-Kähler 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. 1 Important notice: After the first submission of this paper to the arXiv, we have realized that the main result presented in it was implicitly contained in Ref. [10], as explained in Section 2 of Ref. [15], something neither we nor the experts we consulted before the submission were aware of. While this paper cannot be published in a regular scientific journal, we think it still can be useful for the scientific community. b E-mail: Samuele.Chimento [at] csic.es c E-mail: Tomas.Ortin [at] csic.es

Cambridge University Press eBooks, Apr 7, 2015

arXiv (Cornell University), May 31, 2016

We study the gauging of maximal d = 8 supergravity using the embedding tensor formalism. We focus... more 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, 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. [6] by dimensional reduction of the so called "massive 11-dimensional supergravity" proposed by Meessen and Ortín in Ref. [7] are indeed related by an SL(2, R) duality even though they have two completely different 11-dimensional origins.

arXiv (Cornell University), Dec 25, 2020

We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring ef... more 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 α , 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. We study explicitly a non-extremal, charged, black ring solution of pure N = 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory. This work is a first step towards the derivation of the first law at first order in α 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.

Journal of High Energy Physics

Motivated by the current research of generalized symmetries and the construction of conserved cha... more 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.

AIP Conference Proceedings, 2001

Journal of High Energy Physics, 2017

We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for... more We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the Kähler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple secondorder 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 3parameter 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-Nordström-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 Gödel universe and a few potentially homogenous solutions. A key rôle in finding these solutions is played by our ability to write AdS 5 's Kähler base space (CP 2 or SU(1, 2)/U(2)) is three different, yet simple, forms associated to three different isometries. Furthermore, our ansatz for the Kähler metric also allows us to study the dimensional compactification of the theory and its solutions in a systematic way.

Physics Letters B, 1989

Introducing a geometric normal ordering, we give a proof of BRST invariance of the states associa... more Introducing a geometric normal ordering, we give a proof of BRST invariance of the states associated to an arbitrary genus Riemann surface with a puncture, in the operator formalism. FTUAM/88-35 * Work supported in part by the program 'Ayudas para estancias breves en centros de investigación de España y el extranjero', (Comunidad Autónoma de Madrid).

Journal of High Energy Physics

We study the thermodynamics of the 4-dimensional electrically charged black-hole solutions of the... more 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.

Journal of High Energy Physics

Using Wald’s formalism, we study the thermodynamics (first laws and Smarr formulae) of asymptotic... more 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 their thermodynamics.

Journal of High Energy Physics

We construct the Komar integral for axion-dilaton gravity using Wald’s formalism and momentum map... more 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.

Journal of High Energy Physics, 2021

We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvatur... more We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence betweenf(R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables (pressures) and we give a general expression for their conjugate potentials (volumes).

Journal of High Energy Physics, 2021

A correction to this paper has been published: https://doi.org/10.1007/JHEP06(2020)106

Journal of High Energy Physics, 2021

We prove the first law of black hole mechanics in the context of the Heterotic Superstring effect... more We prove the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in α′, 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. We study explicitly a non-extremal, charged, black ring solution of pure mathcalN\mathcal{N}mathcalN N = 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory.This work is a first step towards the derivation of the first law at first order in α′ where, more complicated, non-Abelian, Lorentz (“gravitational”) and ...