Francisco Nettel

Brighter Branes, enhancement of photon production by strong magnetic fields in the gauge/gravity correspondence

A bstractWe use the gauge/gravity correspondence to calculate the rate of photon production in a strongly coupled

Conformal Gauge Transformations in Thermodynamics

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UV dimensional reduction to two from group valued momenta

= 4 plasma in the presence of an intense magnetic field. We start by constructing a family of back reacted geometries that include the black D3-brane solution, as a smooth limiting case for B = 0, and extends to backgrounds with an arbitrarily large constant magnetic field. This family provides the gravitational dual of a field theory in the presence of a very strong magnetic field which intensity can be fixed as desired and allows us to study its effect on the photon production of a quark-gluon plasma. The inclusion of perturbations in the electromagnetic field on these backgrounds is consistent only if the metric is perturbed as well, so we use methods developed to treat operator mixing to manage these general perturbations. Our results show a clear enhancement of photon production with a significant anisotropy, which, in qualitative agreement with the experiments of heavy ion collisions, is particularly noticeable for low P.

Rainbows without unicorns: metric structures in theories with modified dispersion relations

In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its curvature is not and, therefore, neither is the associated pseudo-Riemannian geometry. We claim that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all of the elements of the geometric structure of the thermodynamic phase space change under a re-scaling of the connection one-form. We call this transformation of the geometric structure a conformal gauge transformation. As an example, we revisit the change of the thermodynamic representation and consider the resulting change between the two metrics on the thermodynamic phase space, which induce Weinhold’s energy metric and Ruppeiner’s entropy metric. As a by-product, we obtain a proof of the well-known conformal relation between Weinhold’s and Ruppeiner’s metrics along the equilibrium directions. Finally, we find interesting properties of the almost para-contact structure and of its eigenvectors, which may be of physical interest.

Topological spectrum of mechanical systems

Abstract We describe a new model of deformed relativistic kinematics based on the group manifold U ( 1 ) × S U ( 2 ) as a four-momentum space. We discuss the action of the Lorentz group on such space and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by two energy scales λ and κ. A relevant feature of the model is that it exhibits a running spectral dimension d s with the characteristic short distance reduction to d s = 2 found in most quantum gravity scenarios.

The zeroth law in quasi-homogeneous thermodynamics and black holes

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.

Deformed phase spaces with group valued momenta

We consider the method of topological quantization for conservative systems with a finite number of degrees of freedom. Maupertuis’ formalism for classical mechanics provides an appropriate scenario which permit us to adapt the method of topological quantization, originally formulated for gravitational field configurations. We show that any conservative system in classical mechanics can be associated with a principal fiber bundle. As an application of topological quantization we derive expressions for the topological spectra of some simple mechanical systems and show that they reproduce the discrete behavior of the corresponding canonical spectra.

Topological spectrum of classical configurations

Abstract Motivated by black holes thermodynamics, we consider the zeroth law of thermodynamics for systems whose entropy is a quasi-homogeneous function of the extensive variables. We show that the generalized Gibbs–Duhem identity and the Maxwell construction for phase coexistence based on the standard zeroth law are incompatible in this case. We argue that the generalized Gibbs–Duhem identity suggests a revision of the zeroth law which in turns permits to reconsider Maxwells construction in analogy with the standard case. The physical feasibility of our proposal is considered in the particular case of black holes.

Conformally invariant thermodynamics of a Maxwell-Dilaton black hole

We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the

Two-Dimensional Einstein Manifolds in Geometrothermodynamics

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