Aspects of duality in gravitational theories

Abstract

This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an action manifestly invariant under duality rotations in presence of both electric and magnetic external sources. It is also shown how, in the reduced phase-space, all higher spin gauge fields can be written as bi-hamiltonian systems. The role of the second hamiltonian is played by the electromagnetic duality generator. The second part is devoted to the study of asymptotic symmetries and their applications to holography. After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In particular, it is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. The first applications are studied: an exact representation by bulk vector fields of the asymptotic symmetry algebra through the introduction of a modified Lie bracket, the derivation of how this symmetry algebra is realized on solution space and the construction of the associated centrally extended surface charge algebra.