Structure of the field equations in N = 1 chiral supergravity

TL;DR

This paper analyzes the linearized field equations of N=1 chiral supergravity with a complex tetrad, aiming to understand the coupling to matter and the structure of supersymmetry transformations.

Contribution

It provides a detailed study of the linearized equations and constructs a SUSY-invariant Lagrangian at the linear level for N=1 chiral supergravity.

Findings

Coupling of real and imaginary parts of the tetrad to matter fields.

Construction of a SUSY-invariant Lagrangian at zeroth order.

Comparison of linearized equations with the constructed Lagrangian.

Abstract

We study the structure of linearized field equations in $N = 1$ chiral supergravity (SUGRA) with a complex tetrad, as a preliminary to introducing additional auxiliary fields in order that the supersymmetry (SUSY) algebra close off shell. We follow the first-order formulation we have recently constructed using the method of the usual $N = 1$ SUGRA. In particular, we see how the real and imaginary parts of the complex tetrad are coupled to matter fields in the weak field approximation. Starting from the linearized (free) theory of $N = 1$ chiral SUGRA, we then construct a Lagrangian which is invariant under local SUSY transformations to zeroth order of the gravitational constant, and compare the results with the linearized field equations.