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

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 Λ. From a group-theoretical point of view this means in particular the vanishing of the OSp(N |4)-supercurvatures at the boundary.

$$ \mathcal{N} $$ -extended D = 4 supergravity, unconventional SUSY and graphene

“…We therefore do not consider here boundary terms depending on the scalar fields of the N -extended AdS 4 -supergravity. For pure N = 2, where scalar fields are not present, this choice of asymptotic symmetry is consistent with the analysis of [18], applied in [12].…”

The quantum theory of Chern-Simons supergravity

“…Note Recently, some of us reconsidered, in [13], the Achucarro-Townsend theory [9] and the correspondence (2.1) for the special case N = p = 2, q = 0. In particular, the field equations of the N = 2 AdS 3 supergravity were found as asymptotic boundary conditions on the supergravity field-strengths of N = 2 AdS 4 pure supergravity, along the lines discussed in [14].…”

On supersymmetry, boundary actions and brane charges

“…To find the corresponding improvement it is useful to note that the fermionic fields of V ′ and W are related by 18) and similarly for the ζ variation. We then find that the supercurrents should be improved according to…”

“…Much attention was also given to the study of supergravity in spaces with boundaries. This includes applications to the strong coupling limit of E 8 × E 8 heterotic string theory [12], supersymmetric Randall-Sundrum models [13] and general study of supergravity in various dimensions [14][15][16][17][18].…”