Canonical approach to 2D supersymmetric WZNW model coupled to supergravity

Starting from the known representation of the Kac-Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac-Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy-momentum tensor $L_\pm$ and $G_\pm$ play the role of the diffeomorphisms and supersymmetries generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.Comment: LaTeX, 13 page

Pontryagin Term and Magnetic Mass in 4D AdS Gravity

Indexación: Scopus.In the context of the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, 4D AdS gravity is suitably renormalized by adding the Gauss Bonnet term to the Einstein-Hilbert action. The subsequent addition of the Pontryagin term, with a specific coupling, allows to write the on-shell action in terms of the Weyl tensor and its dual, such that the action becomes stationary for asymptotic (anti) self-dual solutions in the Weyl tensor. The addition to the action of both topological invariants mentioned above does not modify the bulk dynamics, but it does modify the expression of the Noether current and, therefore, the conserved quantities of the theory. Here, we show that the method of Iyer and Wald leads to a fully-covariant Noether charge, which contains both the electric and magnetic parts of the Weyl tensor. For configurations which are globally (anti) self-dual in the Weyl tensor, both the action and the Noether charge identically vanish. This means that, for such spacetimes, the magnetic mass is equal to the electric mass. © Published under licence by IOP Publishing Ltd.This work was funded in part by FONDECYT Grants No. 1131075, 1140296 and 1151107, CONICYT Grant DPI 2014-0115, UNAB Grants DI-735-15/R and DI-1336-16/RG and VRIEA-PUCV Grant 039.345/2016. R.Araneda received financial support from Facultad de Física, Pontificia Universidad Católica de Chile to participate in SOCHIFI Congress.https://iopscience.iop.org/article/10.1088/1742-6596/1043/1/01201

Non-linear screening of external charge by doped graphene

We solve a nonlinear integral equation for the electrostatic potential in doped graphene due to an external charge, arising from a Thomas-Fermi (TF) model for screening by graphene's $\pi$ electron bands. In particular, we study the effects of a finite equilibrium charge carrier density in graphene, non-zero temperature, non-zero gap between graphene and a dielectric substrate, as well as the nonlinearity in the band density of states. Effects of the exchange and correlation interactions are also briefly discussed for undoped graphene at zero temperature. Nonlinear results are compared with both the linearized TF model and the dielectric screening model within random phase approximation (RPA). In addition, image potential of the external charge is evaluated from the solution of the nonlinear integral equation and compared to the results of linear models. We have found generally good agreement between the results of the nonlinear TF model and the RPA model in doped graphene, apart from Friedel oscillations in the latter model. However, relatively strong nonlinear effects are found in the TF model to persist even at high doping densities and large distances of the external charge.Comment: 12 pages including 6 figure

Energy in higher-derivative gravity via topological regularization

Indexación: Scopus.We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein's equations. We focus on the theory in four dimensions, in the presence of a negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method is qualitatively different due to the fact that it is intrinsically nonlinear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions such as gravitational waves in AdS, for which we also find results that are in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory. © 2018 authors. Published by the American Physical Society.https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.04404

Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns

An exhaustive classification of certain class of static solutions for the five-dimensional Einstein-Gauss-Bonnet theory in vacuum is presented. The class of metrics under consideration is such that the spacelike section is a warped product of the real line with a nontrivial base manifold. It is shown that for generic values of the coupling constants the base manifold must be necessarily of constant curvature, and the solution reduces to the topological extension of the Boulware-Deser metric. It is also shown that the base manifold admits a wider class of geometries for the special case when the Gauss-Bonnet coupling is properly tuned in terms of the cosmological and Newton constants. This freedom in the metric at the boundary, which determines the base manifold, allows the existence of three main branches of geometries in the bulk. For negative cosmological constant, if the boundary metric is such that the base manifold is arbitrary, but fixed, the solution describes black holes whose horizon geometry inherits the metric of the base manifold. If the base manifold possesses a negative constant Ricci scalar, two different kinds of wormholes in vacuum are obtained. For base manifolds with vanishing Ricci scalar, a different class of solutions appears resembling "spacetime horns". There is also a special case for which, if the base manifold is of constant curvature, due to certain class of degeneration of the field equations, the metric admits an arbitrary redshift function. For wormholes and spacetime horns, there are regions for which the gravitational and centrifugal forces point towards the same direction. All these solutions have finite Euclidean action, which reduces to the free energy in the case of black holes, and vanishes in the other cases. Their mass is also obtained from a surface integral.Comment: 31 pages, 1 figure, minor changes and references added. Final version to be published in PR

Torsion induces Gravity

In this work the Poincare-Chern Simons and Anti de Sitter Chern Simons gravities are studied. For both a solution that can be casted as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions respectively.Comment: 4 pages, RevTe

Thermodynamics of Taub-NUT/Bolt-AdS Black Holes in Einstein-Gauss-Bonnet Gravity

We give a review of the existence of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity with the parameter $\alpha$ in six dimensions. Although the spacetime with base space $S^{2}\times S^{2}$ has curvature singularity at $r=N$, which does not admit NUT solutions, we may proceed with the same computations as in the $\mathbb{CP}^{2}$ case. The investigation of thermodynamics of NUT/Bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole. Then the validity of the first law of thermodynamics is demonstrated. It is shown that in NUT solutions all thermodynamic quantities for both base spaces are related to each other by substituting $\alpha^{\mathbb{CP}^{k}}=[(k+1)/k]\alpha^{S^{2} \times S^{2}\times >...S_{k}^{2}}$. So no further information is given by investigating NUT solution in the $S^{2}\times S^{2}$ case. This relation is not true for bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made using a new method based on the Gibbs-Duhem relation and Gibbs free energy for NUT solutions. According to this method, the finite action in Einstein Gauss-Bonnet is obtained by considering the generalized finite action in Einstein gravity with an additional term as a function of $\alpha$. Stability analysis is done by investigating the heat capacity and entropy in the allowed range of $\alpha$, $\Lambda$ and $N$. For NUT solutions in $d$ dimensions, there exist a stable phase at a narrow range of $\alpha$. In six-dimensional Bolt solutions, metric is completely stable for $\mathcal{B}=S^{2}\times S^{2}$, and is completely unstable for $\mathcal{B}=\mathbb{CP}^{2}$ case.Comment: 19 pages, 3 figures, some Refs. are added, Fig 1 is replaced, and some corrections are don

Counterterms, Kounterterms, and the variational problem in AdS gravity

Indexación: Scopus.We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson’s theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except for the logarithmic divergence associated with the holographic conformal anomaly, and finite local terms. © 2020, The Author(s).https://link-springer-com.recursosbiblioteca.unab.cl/article/10.1007%2FJHEP08%282020%2906