Supersymmetry algebra in N = 1 chiral supergravity

TL;DR

This paper derives explicit supersymmetry transformation rules and their algebra in N=1 chiral supergravity with a complex tetrad, extending the understanding of SUSY structures in this formulation.

Contribution

It provides the explicit form of SUSY transformations and their on-shell algebra in N=1 chiral supergravity, using a method analogous to standard N=1 SUGRA.

Findings

Explicit SUSY transformation rules in first-order form

On-shell commutator algebra of SUSY transformations

Differences from 2-form gravity parameter constraints

Abstract

We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian for $N = 1$ supergravity (SUGRA) with the complex tetrad following the method used in the usual $N = 1$ SUGRA, and present the explicit form of the SUSY trasformations in the first-order form. The SUSY transformations are generated by two independent Majorana spinor parameters, which are apparently different from the constrained parameters employed in the method of the 2-form gravity. We also calculate the commutator algebra of the SUSY transformations on-shell.