Boundary conditions in supergravity on a manifold with boundary

TL;DR

This paper discusses the importance of boundary conditions in maintaining supersymmetry in five-dimensional supergravity theories on manifolds with boundaries, proposing a simplified boundary action that reduces the need for boundary conditions.

Contribution

It introduces a bulk-plus-boundary action for 5D supergravity that is supersymmetric with fewer boundary conditions, clarifying boundary/orbifold picture correspondence.

Findings

Reduced boundary conditions needed for supersymmetry

Explicit boundary action with Gibbons-Hawking-like term

Clarification of boundary/orbifold picture correspondence

Abstract

We explain why it is necessary to use boundary conditions in the proof of supersymmetry of a supergravity action on a manifold with boundary. Working in both boundary (``downstairs'') and orbifold (``upstairs'') pictures, we present a bulk-plus-boundary/brane action for the five-dimensional (on-shell) supergravity which is supersymmetric with the use of fewer boundary conditions than were previously employed. The required Gibbons-Hawking-like Y-term and many other aspects of the boundary/orbifold picture correspondence are discussed.