Superalgebra and Conservative Quantities in N=1 Self-dual Supergravity

TL;DR

This paper explores the algebraic structure of N=1 self-dual supergravity, demonstrating how its symmetries lead to conserved quantities that form a super-Poincaré algebra, supporting their physical interpretations.

Contribution

It establishes the super-Poincaré algebra structure from the symmetries and conserved charges in N=1 self-dual supergravity, extending previous results in complex gravity.

Findings

SU(2) charges and supercharges form a super-Poincaré algebra.

Energy-momentum and charges are generally covariant.

Supports the physical interpretation of conserved quantities.

Abstract

The N=1 self-dual supergravity has SL(2,C) and the left-handed and right -handed local supersymmetries. These symmetries result in SU(2) charges as the angular-momentum and the supercharges. The model possesses also the invariance under the general translation transforms and this invariance leads to the energy-momentum. All the definitions are generally covariant . As the SU(2) charges and the energy-momentum we obtained previously constituting the 3-Poincare algebra in the Ashtekar's complex gravity, the SU(2) charges, the supercharges and the energy-momentum here also restore the super-Poincare algebra, and this serves to support the reasonableness of their interpretations.