The boundary problem in (super)gravity from a geometric perspective

Speaker: Prof. Lucrezia Ravera, Department of Applied Science and Technology, Torino, Italy

Abstract: I will discuss the boundary problem in gravity and supergravity, retracing the geometric construction of four-dimensional (super)gravity Lagrangians with negative cosmological constant on a manifold with boundary. The presence of a spacetime boundary breaks diffeomorphisms (and supersymmetry) invariance of the action. To recover such invariance, it is necessary to modify the theory by adding appropriate boundary contributions to the Lagrangian, which, in the gravity case, correspond to the Euler-Gauss-Bonnet term and, in supergravity, to its supersymmetric extension. The full Lagrangian can be recast in a MacDowell-Mansouri form. Regarding the supergravity side, I will also consider the case of vanishing cosmological constant in the presence of a non-trivial boundary, where the inclusion of boundary terms involving additional fields, which behave as auxiliary fields for the bulk theory, allows to restore supersymmetry. I will eventually report on the application of the results to specific problems regarding cases where the boundary is located asymptotically.