Twistors and Spin 3/2 Potentials in Quantum Gravity

TL;DR

This paper investigates boundary conditions for various spin fields in quantum gravity, focusing on their preservation under spin-raising/lowering operators and the implications for supergravity on a 3-sphere boundary.

Contribution

It derives conditions for boundary preservation of spin fields and analyzes supergravity boundary conditions on a 3-sphere, highlighting flat Euclidean backgrounds.

Findings

Boundary conditions preserved only in flat Euclidean space

Spin-raising/lowering operators maintain boundary conditions under specific conditions

Alternative supergravity boundary conditions involving gravitino spinor-valued 1-forms

Abstract

Local boundary conditions involving field strengths and the normal to the boundary, originally studied in anti-de Sitter space-time, have been recently considered in one-loop quantum cosmology. This paper derives the conditions under which spin-lowering and spin-raising operators preserve these local boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component spinor analysis of the four potentials of the totally symmetric and independent field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It is shown that such boundary conditions can only be imposed in a flat Euclidean background, for which the gauge freedom in the choice of the potentials remains. Alternative boundary conditions for supergravity involving the spinor-valued 1-forms for gravitinos and the normal to the boundary are also studied.