N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density

TL;DR

This paper constructs an N=3 chiral supergravity theory compatible with reality conditions, deriving its Lagrangian from standard supergravity and exploring extensions to higher N theories like N=4 and N=8.

Contribution

It provides a novel N=3 chiral supergravity formulation with a compatible Lagrangian and discusses extensions to higher N supergravities.

Findings

Derived N=3 chiral supergravity Lagrangian consistent with reality conditions.

Identified non-minimal four-fermion contact terms from supersymmetry invariance.

Explored implications for higher N supergravity theories, including N=4 and N=8.

Abstract

We obtain N = 3 chiral supergravity (SUGRA) compatible with the reality condition by applying the prescription of constructing the chiral Lagrangian density from the usual SUGRA. The $N = 3$ chiral Lagrangian density in first-order form, which leads to the Ashtekar's canonical formulation, is determined so that it reproduces the second-order Lagrangian density of the usual SUGRA especially by adding appropriate four-fermion contact terms. We show that the four-fermion contact terms added in the first-order chiral Lagrangian density are the non-minimal terms required from the invariance under first-order supersymmetry transformations. We also discuss the case of higher N theories, especially for N = 4 and N = 8.