UV dimensional reduction to two from group valued momenta

We describe a new model of deformed relativistic kinematics based on the group manifold $U(1) \times SU(2)$ as a four-momentum space. We discuss the action of the Lorentz group on such space and 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 {\it two} energy scales $\lambda$ and $\kappa$. 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.Comment: 15 pages, 1 figur

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

We use the gauge/gravity correspondence to calculate the rate of photon production in a strongly coupled N=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.Comment: This paper was replaced including metric perturbations for consistency of the calculation, and reports important qualitative changes. 43 page

Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with 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, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.Comment: 10 pages. Discussion on the role of connections was added. Matches published versio

Conformal Gauge Transformations in Thermodynamics

In this work we consider conformal gauge transformations of the geometric structure of thermodynamic fluctuation theory. In particular, we show that the Thermodynamic Phase Space is naturally endowed with a non-integrable connection, defined by all those processes that annihilate the Gibbs 1-form, i.e. reversible processes. Therefore the geometry of reversible processes is invariant under re-scalings, that is, it has a conformal gauge freedom. Interestingly, as a consequence of the non-integrability of the connection, its curvature is not invariant under conformal gauge transformations and, therefore, neither is the associated pseudo-Riemannian geometry. We argue that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all the elements of the geometric structure of the Thermodynamic Phase Space change under 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

Arguing for Principles in Different Legal Cultures

In all legal systems lawyers and judges appeal to general principles. These principles supposed to be taken from the very grounds of Justice. Accordingly they are presented as setting forth such an argument that it should defeat the opponent’s. In this paper I will be interested in the principle of legal certainty and in how it is is understood in Anglo-Saxon and a Continental legal cultures