Tensor calculus for supergravity on a manifold with boundary

TL;DR

This paper extends supergravity tensor calculus to manifolds with boundaries, enabling supersymmetric bulk-plus-boundary actions without boundary conditions, improving upon previous orbifold supergravity methods.

Contribution

It introduces a method to construct supersymmetric actions on manifolds with boundaries using tensor calculus, without needing boundary conditions on off-shell fields.

Findings

Extended F-density formula for boundary actions

Decomposition into co-dimension one submultiplets

Supersymmetric York-Gibbons-Hawking boundary term

Abstract

Using the simple setting of 3D N=1 supergravity, we show how the tensor calculus of supergravity can be extended to manifolds with boundary. We present an extension of the standard F-density formula which yields supersymmetric bulk-plus-boundary actions. To construct additional separately supersymmetric boundary actions, we decompose bulk supergravity and bulk matter multiplets into co-dimension one submultiplets. As an illustration we obtain the supersymmetric extension of the York-Gibbons-Hawking extrinsic curvature boundary term. We emphasize that our construction does not require any boundary conditions on off-shell fields. This gives a significant improvement over the existing orbifold supergravity tensor calculus.