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We provide a realization of the AdS 2 /CFT 1 correspondence in terms of asymptotic symmetries of the AdS 2 ×S 1 and AdS 2 ×S 2 geometries arising in near-extremal BTZ and Reissner-Nordström black holes. Cardy's formula exactly accounts for the deviation of the Bekenstein-Hawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality. * jnavarro@lie.uv.es † pnavarro@lie.uv.es

A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central) 1/(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.

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The extension of the adiabatic regularization method to spin-1/2 fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-1/2 fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.

Motivated by the quest for black holes in AdS braneworlds, and in particular by the holographic conjecture relating 5D classical bulk solutions with 4D quantum corrected ones, we numerically solve the semiclassical Einstein equations (backreaction equations) with matter fields in the (zero temperature) Boulware vacuum state. In the absence of an exact analytical expression for T µν in four dimensions we work within the s-wave approximation. Our results show that the quantum corrected solution is very similar to Schwarzschild till very close to the horizon, but then a bouncing surface for the radial function appears which prevents the formation of an event horizon. We also analyze the behavior of the geometry beyond the bounce, where a curvature singularity arises. In the dual theory, this indicates that the corresponding 5D static classical braneworld solution is not a black hole but rather a naked singularity.

We point out that if quantum field renormalization is taken into account, and the counterterms are evaluated at the Hubble-radius crossing time or few e-foldings after it, the predictions of slowroll inflation for both the scalar and tensorial power spectrum change significantly. This leads to a change in the consistency condition that relates the tensor-to-scalar amplitude ratio with spectral indices. A reexamination of the potentials φ 2 , φ 4 , shows that both are compatible with five-year WMAP data. Only when the counterterms are evaluated at much larger times beyond the end of inflation one recovers the standard predictions. The alternative predictions presented here may soon come within the range of measurement of near-future experiments.PACS numbers: 98.80.Cq A sufficiently long period of accelerated expansion in the very early universe is able to solve the questions raised by the standard big bang cosmology [1]. The hot big bang cosmology is an extremely successful theory. It explains the existence of the cosmic microwave background (CMB) and its thermal nature, the observed expansion of the universe, the abundance of light elements and the astrophysical fits for the age of the universe. However, it leaves without answer why our universe appears so homogeneous and nearly flat at large scales. Inflation offers a natural answer to these questions and, at the same time, provides a predictive mechanism to account for the small observed inhomogeneities [2] responsible for the structure formation in the universe and the anisotropies present in the cosmic microwave background (CMB), as first detected by the COBE satellite and further analyzed by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite [3]. Inflation predicts production of primordial density perturbations and relic gravitational waves as amplifications of vacuum fluctuations together with a quantum-to-classical transition at the scale of Hubble sphere crossing. Primordial perturbations leave an imprint in the CMB anisotropies, which are, therefore, of major importance for understanding our universe and its origin. The potential-energy density of a scalar (inflaton) field is assumed to cause the inflationary expansion, and the amplification of its quantum fluctuations and those of the metric are inevitable consequences in an expanding universe [4]. The metric fluctuations provide the initial conditions for the acoustic oscillations of the plasma at the onset of the subsequent radiation-dominated epoch. The detection of the effects * Electronic address: ivan.agullo@uv.es † Electronic address: jnavarro@ific.uv.es ‡ Electronic address: olmo@iem.cfmac.csic.es § Electronic address: leonard@uwm.edu of primordial gravitational waves in future high-precision measurements of the CMB anisotropies, as for instance in the PLANCK satellite mission [5], will serve as a highly non-trivial test for inflation. Therefore, it is particularly important to scrutinize, from all points of view, the standard predictions of inflation (as summarized for instance, in [6])...

We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to improve the adiabatic regularization/renormalization scheme. We provide details on the application of the method for Dirac fields living in a four-dimensional Friedmann-Lemaître-Robertson-Walker spacetime with a Yukawa coupling to an external scalar field. We check the consistency of our proposal by working out the conformal anomaly. We also analyze a two-dimensional Dirac field in Minkowski space coupled to a homogeneous electric field and reproduce the known results on the axial anomaly. The adiabatic expansion of the modes given here can be used to properly characterize the allowed physical states of the Dirac fields in the above external backgrounds.