SU(2) Charges as Angular-momentum in N=1 Self-dual Supergravity

TL;DR

This paper explores how SU(2) charges in N=1 self-dual supergravity can be understood as angular-momentum, highlighting their conserved, gauge-invariant nature and algebraic structure.

Contribution

It demonstrates that SU(2) charges in N=1 self-dual supergravity can be interpreted as angular-momentum with an su(2) algebraic structure, extending the understanding of symmetries in supergravity.

Findings

SU(2) charges are conserved and gauge covariant.

Charges form an su(2) algebra.

Charges can be interpreted as angular-momentum.

Abstract

The N=1 self-dual supergravity has SL(2.C) symmetry. This symmetry results in SU(2) charges as the angular-momentum. As in the non-supersymmetric self-dual gravity, the currents are also of their potentials and are therefore identically conserved. The charges are generally invariant and gauge covariant under local SU(2) transforms approaching to be rigid at spatial infinity. The Poisson brackets constitute su(2) algebra and hence can be interpreted as the generally covariant conservative angular-momentum.