Agenda de l'ENS de Lyon

This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. In particular, we focus on the minisuperspace reduction where the number of remaining degrees of freedom is finite. This work takes its place in the quest of understanding the role of physical and gauge symmetries in gravity. Consistent efforts have been made in this direction by the study of boundary symmetries. They can turn gauge into physical symmetries, this being related to the appearance of an infinite tower of conserved charges. I choose here a different approach, treating minisuperspaces as mechanical models evolving in one spacetime direction and investigating their classical symmetries. The spacetime will be foliated into homogeneous slices labelled by the evolution parameter.
After presenting the formalism allowing us to describe the reduced models in terms of an action principle, we discuss the condition for having an (extended) conformal symmetry given by the group action (SL(2,R) x R) x R2. The black hole model then enlightens the subtle role of the spacelike boundary of the homogeneous slice, the latter interplaying with the conformal symmetry and being associated to a conserved quantity from the mechanical point of view.
The absence of the infinite tower of charges, characteristic of the full theory, is due here to a symmetry-breaking mechanism. This is made explicit by looking at the infinitedimensional extension of the symmetry group. In particular, this allows looking at the equation of motion of the mechanical system in terms of the infinite-dimensional group, who in turn has the effect of rescaling the coupling constants of the theory.
Finally, the presence of the finite symmetry group allows defining a quantum model in terms of the corresponding representation theory. Requesting its protection in a modified effective theory would provide a powerful tool to discriminate between different ways of accounting for the quantum effects. In the end, the conformal invariance of the black hole background opens the door to its holographic properties and might have important consequences on the study of the propagation of test fields on it and the corresponding perturbation theory.