We consider a class of warped higher dimensional brane models with topology M × Σ × S 1 /Z2, where Σ is a D2 dimensional manifold. Two branes of codimension one are embedded in such a bulk space-time and sit at the orbifold fixed points. We concentrate on the case where an exponential warp factor (depending on the distance along the orbifold) accompanies the Minkowski M and the internal space Σ line elements. We evaluate the moduli effective potential induced by bulk scalar fields in these models, and we show that generically this can stabilize the size of the extra dimensions. As an application, we consider a scenario where supersymmetry is broken not far below the cutoff scale, and the hierarchy between the electroweak and the effective Planck scales is generated by a combination of redshift and large volume effects. The latter is efficient due to the shrinking of Σ at the negative tension brane, where matter is placed. In this case, we find that the effective potential can stabilize the size of the extra dimensions (and the hierarchy) without fine tuning, provided that the internal space Σ is flat.

We examine the lowest order quantum corrections to the effective action arising from a quantized real scalar field in the Randall-Sundrum background spacetime. The leading term is the familiar vacuum, or Casimir, energy density. The next term represents an induced gravity term that can renormalize the 4-dimensional Newtonian gravitational constant. The calculations are performed for an arbitrary spacetime dimension. Two inequivalent boundary conditions, corresponding to twisted and untwisted field configurations, are considered. A careful discussion of the regularization and renormalization of the effective action is given, with the relevant counterterms found. It is shown that the requirement of self-consistency of the Randall-Sundrum solution is not simply a matter of minimizing the Casimir energy density. The massless, conformally coupled scalar field results are obtained as a special limiting case of our results. We clarify a number of differences with previous work.

Black hole quasinormal frequencies are complex numbers that encode information on how a black hole relaxes after it has been perturbed and depend on the features of the geometry and on the type of perturbations. On the one hand, the examples studied so far in the literature focused on the case of black hole geometries with singularities in their interior. On the other hand, it is expected that quantum or classical modifications of general relativity may correct the pathological singular behavior of classical black hole solutions. Despite the fact that we do not have at hand a complete theory of quantum gravity, regular black hole solutions can be constructed by coupling gravity to an external form of matter, sometimes modeled by one form or another of nonlinear electrodynamics. It is therefore relevant to compute quasinormal frequencies for these regular solutions and see how differently, from the ordinary ones, regular black holes ring. In this paper, we take a step in this direction and, by computing the quasinormal frequencies, study the quasinormal modes of neutral and charged scalar field perturbations on regular black hole backgrounds in a variety of models.

The lowest order quantum corrections to the effective action arising from quantized massive fermion fields in the Randall-Sundrum background spacetime are computed. The boundary conditions and their relation with gauge invariance are examined in detail. The possibility of Wilson loop symmetry breaking in brane models is also analysed. The self-consistency requirements, previously considered in the case of a quantized bulk scalar field, are extended to include the contribution from massive fermions. It is shown that in this case it is possible to stabilize the radius of the extra dimensions but it is not possible to simultaneously solve the hierarchy problem, unless the brane tensions are dramatically fine tuned, supporting previous claims.Comment: 25 pages, 1 figure, RevTe

In this paper we discuss the possibility that chiral phase transitions, analogous to those of QCD, occur in the vicinity of a black hole. If the black hole is surrounded by a gas of strongly interacting particles, an inhomogeneous condensate will form. We demonstrate this by explicitly constructing self-consistent solutions.According to the theory of quantum fields in curved space, black holes radiate energy at a temperature inversely proportional to their mass [1]. As the black hole evaporates, its temperature rises, and at some point a bubble of a high temperature phase surrounding the horizon may form, if a phase transition occurs. This was a particularly interesting phenomena in connection with the Higgs model of electroweak symmetry breaking and its study requires the inclusion of interactions, being an essential feature of the phase transition. A method to deal with this situation was proposed, but the indication was that, in the Higgs model, the associated high temperature phase would be too localized around the black hole, so that symmetry, effectively, would not be restored [2]. The same problem has been reconsidered by Moss taking into account the effect of trapped particles, i.e. particles emitted by the black hole and reflected back by the walls of the bubble. He indicated that, for some class of bag models, the picture may change and lead to a transient equilibrium configuration of restored symmetry phase, localized around the black hole [3].A field in which the similar problem of understanding the phase structure is nowadays very topical is that of QCD at finite temperature and density, in which phenomena like chiral symmetry breaking and confinement/deconfinement transitions are known to take place. In this context, the natural way of addressing the problem would be to use 'first principle' non-perturbative lattice methods, but already in flat space, and especially at high densities, things become prohibitive. In lack of a first principle approach, approximating QCD with a strongly interacting fermion effective field theories comes in handy. The price to pay is that we have to work with a non-renormalizable effective theory, but with the bonus of dealing with a simpler one that shares many of the essential properties of QCD. As a matter of fact, a great deal of attention is currently paid on mapping various phases on the temperature-density diagram within such an effective field theoretical approach, in order to gain understanding of the vacuum structure of strongly interacting matter (See Ref.[4] for a recent review).The aim of this work is to use the same simplification of degrading QCD to a non-renormalizable, strongly interacting fermion effective field theory, and study the interplay with black holes. To begin with, we wish to consider a little more in detail the issue of phase transitions that would break or restore chiral symmetry. In the context of strongly interacting fermionic systems, it is well known that chiral symmetry breaking takes place, and this fact is discussed in terms of the ...