AdS(2)/CFT1 correspondence and near-extremal black hole entropy

We provide a realization of the AdS 2 /CFT 1 correspondence in terms of asymptotic symmetries of the AdS 2× S 1 and AdS 2× S 2 geometries arising in near-extremal BTZ and ReissnerNordström black holes. We evaluate the corresponding central charges and show that Cardy's formula exactly accounts for the deviation of the BekensteinHawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality

Particle creation and the Schwinger model

We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results exactly match in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime.Comment: 10 pages; This article belongs to the Special Issue Black Holes, Cosmology, Quantum Gravity, and Their Symmetries

Conformal and non-conformal symmetries in 2D dilaton gravity

We introduce new extra symmetry transformations for generic 2D dilaton-gravity models. These symmetries are non-conformal but special linear combinations of them turn out to be the extra (conformal) symmetries of the CGHS model and the model with an exponential potential. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an auxiliary invariant metric, we construct one-loop models which maintain the extra symmetry of the classical action. © 1997 Elsevier Science B.V.M. N. is grateful to the Spanish MEC, CSIC and also the IMAFF for a research contract.Peer Reviewe

Canonical Structure of 2D Black Holes

We determine the canonical structure of two-dimensional black-hole solutions arising in $2D$ dilaton gravity. By choosing the Cauchy surface appropriately we find that the canonically conjugate variable to the black hole mass is given by the difference of local (Schwarzschild) time translations at right and left spatial infinities. This can be regarded as a generalization of Birkhoff's theorem.Comment: 8 pages, 1 figure (uuencoded) included, plain Latex, a4, psfig. FTUV/94-23, IFIC/94-21, Imperial-TP/93-93/3

Reflexive functors of modules in commutative algebra

Funtores reflexivos de módulos aparecen de forma natural en Geometría algebraica, principalmente en la teoría de las representaciones lineales de los planes de grupo, y en "teorías de dualidad". En este trabajo se estudian determinados funtores reflexivos de los módulos y ofrecemos muchas propiedades de funtores reflexivos de los módulos, de álgebra y de biálgebras.Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in “duality theories”. In this paper we study and determine reflexive functors of modules and we give many properties of reflexive functors of modules, of algebras and of bialgebras

Affine functors and duality

Un funtor de conjuntos X más de la categoría de álgebras-K conmutativa se dice que es un funtor afín si su funtor de funciones, Aₓ, es reflexiva y X = SpecAₓ. Probamos que funtores afines son igual a un límite directo de los esquemas afines y que los sistemas afines, esquemas formales, la finalización de los planes afines a lo largo de un subesquema cerrado, etc., son funtores afines. Dotar a un funtor afín X con un funtor de estructura monoide equivale a dotar Aₓ con un funtor de estructura biálgebras. Si G es un funtor afín de monoides, entonces A*G es el funtor envolvente de álgebras de G y la categoría de G-módulos es equivalente a la categoría de A*G-módulos. Las aplicaciones de estos resultados incluyen la dualidad Cartier, dualidad Tannakian neutral para los esquemas del grupo afín, la equivalencia entre los grupos formales y álgebras de Lie de característica cero, etc.A functor of sets X over the category of K-commutative algebras is said to be an affine functor if its functor of functions, Aₓ, is reflexive and X = SpecAₓ. We prove that affine functors are equal to a direct limit of affine schemes and that affine schemes, formal schemes, the completion of affine schemes along a closed subscheme, etc., are affine functors. Endowing an affine functor X with a functor of monoids structure is equivalent to endowing Aₓ with a functor of bialgebras structure. If G is an affine functor of monoids, then A∗G is the enveloping functor of algebras of G and the category of G-modules is equivalent to the category of A∗G-modules. Applications of these results include Cartier duality, neutral Tannakian duality for affine group schemes, the equivalence between formal groups and Lie algebras in characteristic zero, etc

A quantum model of Schwarzschild black hole evaporation

We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show that it cannot be a flat metric

Equivalence of adiabatic and DeWitt-Schwinger renormalization schemes

We prove that adiabatic regularization and DeWitt-Schwinger point-splitting provide the same result when renormalizing expectation values of the stress-energy tensor for spin-1/2 fields. This generalizes the equivalence found for scalar fields, which is here recovered in a different way. We also argue that the coincidence limit of the DeWitt-Schwinger proper time expansion of the two-point function agrees exactly with the analogous expansion defined by the adiabatic regularization method at any order (for both scalar and spin-1/2 fields). We also illustrate the power of the adiabatic method to compute higher order DeWitt coefficients in Friedmann-Lemaitre-Robertson-Walker Universes

Spacetime correlators of perturbations in slow-roll de Sitter inflation

Two-point correlators and self-correlators of primordial perturbations in quasi-de Sitter spacetime backgrounds are considered. For large separations two-point correlators exhibit nearly scale invariance, while for short distances self-correlators need standard renormalization. We study the deformation of two-point correlators to smoothly match the self-correlators at coincidence. The corresponding angular power spectrum is evaluated in the Sachs-Wolfe regime of low multipoles. Scale invariance is maintained, but the amplitude of C(l)could change in a nontrivial way

Anti-Doping Knowledge of Students Undertaking Bachelor’s Degrees in Sports Sciences in Spain

In Spain, students pursuing a career in athletic training, physical education, or scientific evaluation of sports enroll in a bachelor's degree in sports sciences. This degree provides knowledge and skills in a broad array of sports settings and promotes research-based interdisciplinary knowledge. However, the student's syllabus rarely includes specific academic training on anti-doping regulations or doping prevention. The purpose of this study was to assess the anti-doping knowledge of the students undertaking a bachelor's degree in sports sciences in Spanish universities. One thousand two hundred and thirty-three bachelor students in sport science (907 males, 322 females, and 4 participants with non-binary sex) from 26 Spanish universities completed a validated questionnaire about general anti-doping knowledge. The questionnaire is an adapted version of the Play True Quiz of the World Anti-Doping Agency and contains 37 multiple-choice questions. The score obtained in the questionnaire was transformed into a 0-100-point scale. The questionnaire was distributed among students within each university by a faculty member and it was filled out online. Students obtained a score of 65.8 +/- 10.10 points (range = 32-92 points). There was an effect of the course in the score obtained (p < 0.001). Students of the first course (63.6 +/- 9.5 points) had lower scores than the remaining courses (p < 0.037) while the students of the fourth course obtained the highest scores (68.7 +/- 9.5 points; p < 0.019). The students with an itinerary on sports performance were the respondents with the highest anti-doping knowledge (67.2 +/- 10.2) points, followed by the students with an itinerary on health (66.7 +/- 9.5 points). The knowledge of basic anti-doping rules and doping prevention strategies of the bachelor students in sports sciences in Spain was suboptimal. Increasing doping prevention information in the syllabus of the bachelor's degree in sports sciences is essential as these future professionals will directly work with populations at risk of doping