N=1 and N=2 pure supergravities on a manifold with boundary

TL;DR

This paper constructs N=1 and N=2 supergravity actions with a boundary, ensuring supersymmetry invariance through topological terms and boundary conditions on field strengths, without fixing boundary fields.

Contribution

It introduces boundary-compatible supergravity actions with topological terms, fixing boundary field strengths dynamically, advancing the understanding of supersymmetry in manifolds with boundary.

Findings

Supersymmetry invariance requires topological boundary terms.

Boundary field strengths are fixed to constant values by dynamics.

Supercurvatures vanish at the boundary, ensuring symmetry.

Abstract

Working in the geometric approach, we construct the lagrangians of N=1 and N=2 pure supergravity in four dimensions with negative cosmological constant, in the presence of a non trivial boundary of space-time. We find that the supersymmetry invariance of the action requires the addition of topological terms which generalize at the supersymmetric level the Gauss-Bonnet term. Supersymmetry invariance is achieved without requiring Dirichlet boundary conditions on the fields at the boundary, rather we find that the boundary values of the fieldstrengths are dynamically fixed to constant values in terms of the cosmological constant \Lambda. From a group-theoretical point of view this means in particular the vanishing of the OSp(N|4)-supercurvatures at the boundary.