Carlos Enrique Valcárcel

Resumo Este trabalho tem como ponto de partida revisitar os célebres teoremas de Noether, com o objetivo de discutir o papel das simetrias de calibre na definição de correntes de Noether não triviais, livres das ambiguidades que afetam tais transformações. Diferentemente das leis de conservação decorrentes do primeiro teorema de Noether, transformações de calibre são, em geral, tratadas no contexto do segundo teorema de Noether, ao qual não se costuma associar quantidades conservadas fisicamente significativas. Contrastando essa concepção, buscamos apresentar um subgrupo particular das transformações de calibre – denominado impróprio – capaz de gerar cargas globalmente definidas na presença de bordas. Para investigar esse fenômeno, adotamos a teoria de Chern–Simons como modelo de análise, especialmente interessante por permitir traçar paralelos entre teorias de calibre não abelianas, como a teoria de Yang–Mills, e a gravitação no contexto do formalismo Hamiltoniano.

We propose a non-relativistic version of the Carroll–Field–Jackiw theory in order to study the breaking of Galilean symmetry induced by the inclusion of an external tensor via Chern–Simons-like term in the Galilean covariant Lagrangian for the massive vector field. The results show that this model allows wave plane solutions with two frequency modes, i.e., it is possible to describe the phenomena of birefringence in the non-relativistic context. We also study the planar regime of this model in the two limits (electric and magnetic) of the usual electromagnetic field, obtaining the generation of topological mass and current of the Galilean fields. Finally, and following the same way, we propose a Podolsky electrodynamics with a Galilean-symmetry breaking term producing also the birefringence.

We propose a non--relativistic version of the Carroll--Field--Jackiw theory in order to study the breaking of Galilean symmetry induced by the inclusion of an external tensor via Chern--Simons--like term in the Galilean covariant Lagrangian for the massive vector field. The results show that this model allows wave plane solutions with two frequency modes, i.e., it is possible to describe the phenomena of birefringence in the non--relativistic context. We also study the planar regime of this model in the two limits (electric and magnetic) of the usual electromagnetic field, obtaining the generation of topological mass and current of the Galilean fields. Finally, and following the same way, we propose a Podolsky electrodynamics with a Galilean--symmetry breaking term producing also the birefringence.

Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain a general form of such diffeomorphisms in Lorentzian and Euclidean signatures and use them to extend known holographic results, including the Schwarzian action on the asymptotic boundary, from JT to a large class of dilaton gravity models.

Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain a general form of such diffeomorphisms in Lorentzian and Euclidean signatures and use them to extend known holographic results, including the Schwarzian action on the asymptotic boundary, from JT to a large class of dilaton gravity models.

We study a bi-parametric family of dilaton gravity models with constant and negative curvature. This family includes the Jackiw–Teitelboim gravity and the Liouville gravity model induced by a bosonic string. Furthermore, this family is conformally equivalent to the hyperbolic dilaton models. We propose boundary conditions in the Fefferman–Graham and in the Eddington–Finkelstein gauge. We check the consistency of the asymptotic conditions by computing the entropy of their black hole solution.

We study a bi-parametric family of dilaton gravity models with constant and negative curvature. This family includes the Jackiw-Teitelboim gravity and the Liouville gravity model induced by a bosonic string. Furthermore, this family is conformally equivalent to the hiperbolic dilaton models. We propose boundary conditions in the Fefferman-Graham and in the Eddington-Finkelstein gauge. We check the consistency of the asymptotic conditions by computing the entropy of their black hole solution.

The dilaton gravity models in two dimensions, including the Jackiw--Teitelboim model and its deformations, are particular cases of Poisson sigma models. Target space diffeomorphisms map one Poisson sigma model to another. We propose to use these diffsomorphisms to identify asymptotic conditions, boundary actions, and asymptotic symmetries in distinct dilaton gravity models. As an example, we use the asymptotic conditions in Jackiw--Teitelboim gravity to construct an asymptotic problem with Virasoro symmetry in a class of asymptotically Rindler models. We show, that the method can be applied to a wide class of pairs of dilaton gravities and discuss possible generalizations.

The dilaton gravity models in two dimensions, including the Jackiw–Teitelboim model and its deformations, are particular cases of Poisson sigma models. Target space diffeomorphisms map one Poisson sigma model to another. We propose to use these diffeomorphisms to identify asymptotic conditions, boundary actions, and asymptotic symmetries in distinct dilaton gravity models. As an example, we use the asymptotic conditions in Jackiw–Teitelboim gravity to construct an asymptotic problem with Virasoro symmetry in a class of asymptotically Rindler models. We show that the method can be applied to a wide class of pairs of dilaton gravities and discuss possible generalizations.

Having in mind extensions of 2D holography beyond the Jackiw-Teitelboim model we propose holographic counterterms and asymptotic conditions for a family of asymptotically AdS₂ dilaton gravity models leading to a consistent variational problem and a finite on-shell action. We show the presence of asymptotic Virasoro symmetries in all these models. The Schwarzian action generates (a part) of the equations of motion governing the asymptotic degrees of freedom. We also analyse the applicability of various entropy formulae. By a dilaton-dependent conformal transformation our results are extended to an even larger class of models having exotic asymptotic behavior. We also analyse asymptotic symmetries for some other classes of dilaton gravities without, however, constructing holographic counterterms.