Dynamics on the Virasoro group, 2D gravity and hidden symmetries

We derive the action of 2D gravity from the two-cocycle of the Virasoro group by using a previously introduced method for constructing a dynamical system from a Lie group. A natural construction and explanation of the hidden SL(2, )-Kac-Moody symmetry, of general applicability, is provided. We also show how the proper quantization goes beyond the ordinary co-adjoint orbit method, and the possible connection with the Poisson-Lie groups.     

Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra

We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the renormalization factor of L(z) Research partially supported by the Conselleria de Cultura de la Generalitat Valenciana, the Plan de Formacion del Personal Investigador, the Comision Asesora de Investigacion Cientifica y Tecnica (CAICYT), and The British Council.     

Hawking radiation by Kerr black holes and conformal symmetry

The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance.     

Inflation,quantum fields,and CMB anisotropies

Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly influences the generation of primordial perturbations and hence the expected measurable imprint of cosmological inflation on the CMB. However, the new predictions remain in agreement with observation, and in fact favor the simplest forms of inflation. In the near future, observations of the influence of gravitational waves from the early universe on the CMB will test our new predictions.     

Quantization on the Virasoro group

The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace _{(c, h)} , the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. _{(c, h)} is a proper subspace of the space of polarized functions for those values ofc andh for which the Kac determinant is zero. We give the local version of these group representations as well as the associated classical phase space structures, i.e., symplectic form and Noether invariants.Research partially supported by the Conselleria de Cultura de la Generalitat Valenciana, the Plan de formación del Personal investigador, the Comision Interministerial de Ciencia y Tecnologia (CICYT) and the British Council     

Black hole radiance, short distances, and TeV gravity

Using a derivation of black hole radiance in terms of two-point functions one can provide a quantitative estimate of the contribution of short distances to the spectrum. Thermality is preserved for black holes with kappalp<1. However, deviations from the Planckian spectrum can be found for mini black holes in TeV gravity scenarios, even before reaching the Planck phase.     

A Planck-Like Problem for Quantum Charged Black Holes

Motivated by the parallelism existing between the puzzles of classical physics at the beginning of the XXth century and the current paradoxes in the search of a quantum theory of gravity, we give, in analogy with Planck's black body radiation problem, a solution for the exact Hawking flux of evaporating Reissner-Nordström black holes. Our results show that when back-reaction effects are fully taken into account the standard picture of black hole evaporation is significantly altered, thus implying a possible resolution of the information loss problem.     

Formal Group Laws for Affine Kac-Moody groups and group quantization

We describe a method for obtaining Formal Group Laws from the structure constants of Affine Kac-Moody groups and then apply a group manifold quantization procedure which permits construction of physical representations by using only canonical structures on the group. As an intermediate step we get an explicit expression for two-cocycles on Loop Groups. The programme is applied to the AffineSU(2) group.Research partially supported by the Conselleria de Cultura de la Generalitat Valenciana, the Plan de Formacion del Personal Investigador, and the Comision Asesora de Investigacion Cientifica y Tecnica (CAICYT)On leave of absence from the IFIC, Centro Mixto Universidad de Valencia — C.S.I.C. and the Departamento de Fisica Teorica de la Universidad de Valencia     

Reexamination of the power spectrum in de Sitter inflation

We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.