The supermultiplet of boundary conditions in supergravity

TL;DR

This paper formulates boundary conditions in supergravity in a manifestly supersymmetric way, linking bulk fields to boundary supercurrents and energy-momentum tensors, with implications for higher-dimensional models.

Contribution

It introduces the Extrinsic Curvature Tensor Multiplet and establishes its relation to boundary supercurrent multiplets in 3D N=1 supergravity, extending to higher dimensions.

Findings

Boundary conditions relate bulk gravitino to boundary supercurrent.

Boundary conditions set the extrinsic curvature tensor multiplet equal to the boundary supercurrent multiplet.

Extension to higher-dimensional models like Randall-Sundrum and Horava-Witten is discussed.

Abstract

Boundary conditions in supergravity on a manifold with boundary relate the bulk gravitino to the boundary supercurrent, and the normal derivative of the bulk metric to the boundary energy-momentum tensor. In the 3D N=1 setting, we show that these boundary conditions can be stated in a manifestly supersymmetric form. We identify the Extrinsic Curvature Tensor Multiplet, and show that boundary conditions set it equal to (a conjugate of) the boundary supercurrent multiplet. Extension of our results to higher-dimensional models (including the Randall-Sundrum and Horava-Witten scenarios) is discussed.