52 research outputs found

### Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

Motivated by possible applications within the framework of anti-de Sitter
gravity/Conformal Field Theory (AdS/CFT) correspondence, charged black holes
with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D
dimensions, and whose electric field is described by a nonlinear
electrodynamics (NED) are studied. For a topological static black hole ansatz,
the field equations are exactly solved in terms of the electromagnetic stress
tensor for an arbitrary NED Lagrangian, in any dimension D and for arbitrary
positive values of Gauss-Bonnet coupling. In particular, this procedure
reproduces the black hole metric in Born-Infeld and conformally invariant
electrodynamics previously found in the literature. Altogether, it extends to
D>4 the four-dimensional solution obtained by Soleng in logarithmic
electrodynamics, which comes from vacuum polarization effects. Fall-off
conditions for the electromagnetic field that ensure the finiteness of the
electric charge are also discussed. The black hole mass and vacuum energy as
conserved quantities associated to an asymptotic timelike Killing vector are
computed using a background-independent regularization of the gravitational
action based on the addition of counterterms which are a given polynomial in
the intrinsic and extrinsic curvatures.Comment: 30 pages, no figures; a few references added; final version for PR

### Irregular Hamiltonian Systems

Hamiltonian systems with linearly dependent constraints (irregular systems),
are classified according to their behavior in the vicinity of the constraint
surface. For these systems, the standard Dirac procedure is not directly
applicable. However, Dirac's treatment can be slightly modified to obtain, in
some cases, a Hamiltonian description completely equivalent to the Lagrangian
one. A recipe to deal with the different cases is provided, along with a few
pedagogical examples.Comment: To appear in Proceedings of the XIII Chilean Symposium of Physics,
Concepcion, Chile, November 13-15 2002. LaTeX; 5 pages; no figure

### Free energy of a Lovelock holographic superconductor

We study thermodynamics of black hole solutions in Lanczos-Lovelock AdS
gravity in d+1 dimensions coupled to nonlinear electrodynamics and a
Stueckelberg scalar field. This class of theories is used in the context of
gauge/gravity duality to describe a high-temperature superconductor in d
dimensions. Larger number of coupling constants in the gravitational side is
necessary to widen a domain of validity of physical quantities in a dual QFT.
We regularize the gravitational action and find the finite conserved quantities
for a planar black hole with scalar hair. Then we derive the quantum
statistical relation in the Euclidean sector of the theory, and obtain the
exact formula for the free energy of the superconductor in the holographic
quantum field theory. Our result is analytic and it includes the effects of
backreaction of the gravitational field. We further discuss on how this formula
could be used to analyze second order phase transitions through the
discontinuities of the free energy, in order to classify holographic
superconductors in terms of the parameters in the theory.Comment: 26 pages, no figures; references added; published versio

### Fluctuations around classical solutions for gauge theories in Lagrangian and Hamiltonian approach

We analyze the dynamics of gauge theories and constrained systems in general
under small perturbations around a classical solution (background) in both
Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory,
described by a quadratic Lagrangian, has the same constraint structure and
number of physical degrees of freedom as the original non-perturbed theory,
assuming the non-degenerate solution has been chosen. We show that the number
of Noether gauge symmetries is the same in both theories, but that the gauge
algebra in the fluctuations theory becomes Abelianized. We also show that the
fluctuations theory inherits all functionally independent rigid symmetries from
the original theory, and that these symmetries are generated by linear or
quadratic generators according to whether the original symmetry is preserved by
the background, or is broken by it. We illustrate these results with the
examples.Comment: 27 pages; non-essential but clarifying changes in Introduction, Sec.
3 and Conclusions; the version to appear in J.Phys.

### Holographic currents in first order Gravity and finite Fefferman-Graham expansions

We study the holographic currents associated to Chern-Simons theories. We
start with an example in three dimensions and find the holographic
representations of vector and chiral currents reproducing the correct
expression for the chiral anomaly. In five dimensions, Chern-Simons theory for
AdS group describes first order gravity and we show that there exists a gauge
fixing leading to a finite Fefferman-Graham expansion. We derive the
corresponding holographic currents, namely, the stress tensor and spin current
which couple to the metric and torsional degrees of freedom at the boundary,
respectively. We obtain the correct Ward identities for these currents by
looking at the bulk constraint equations.Comment: 21 pages; version published in JHE

### Renormalized AdS action and Critical Gravity

It is shown that the renormalized action for AdS gravity in even spacetime
dimensions is equivalent -on shell- to a polynomial of the Weyl tensor, whose
first non-vanishing term is proportional to $Weyl^2$. Remarkably enough, the
coupling of this last term coincides with the one that appears in Critical
Gravity.Comment: 15 pages, references added, version accepted to JHE

### Canonical sectors of five-dimensional Chern-Simons theories

The dynamics of five-dimensional Chern-Simons theories is analyzed. These
theories are characterized by intricate self couplings which give rise to
dynamical features not present in standard theories. As a consequence, Dirac's
canonical formalism cannot be directly applied due to the presence of
degeneracies of the symplectic form and irregularities of the constraints on
some surfaces of phase space, obscuring the dynamical content of these
theories. Here we identify conditions that define sectors where the canonical
formalism can be applied for a class of non-Abelian Chern-Simons theories,
including supergravity. A family of solutions satisfying the canonical
requirements is explicitly found. The splitting between first and second class
constraints is performed around these backgrounds, allowing the construction of
the charge algebra, including its central extension.Comment: 12 pages, no figure

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