Construction of N = 2 Chiral Supergravity Compatible with the Reality Condition

TL;DR

This paper develops a new formulation of N=2 chiral supergravity compatible with reality conditions, enabling Ashtekar's canonical formulation without auxiliary fields or constrained SUSY parameters.

Contribution

It introduces a novel N=2 chiral supergravity framework that is compatible with reality conditions and simplifies the canonical formulation process.

Findings

Formulation is compatible with the reality condition.

Supersymmetry transformation parameters are unconstrained.

Reduces to usual N=2 SUGRA with an imaginary boundary term.

Abstract

We construct N = 2 chiral supergravity (SUGRA) which leads to Ashtekar's canonical formulation. The supersymmetry (SUSY) transformation parameters are not constrained at all and auxiliary fields are not required in contrast with the method of the two-form gravity. We also show that our formulation is compatible with the reality condition, and that its real section is reduced to the usual N = 2 SUGRA up to an imaginary boundary term.