Self-Dual Supergravity Theories in 2+2 Dimensions

TL;DR

This paper constructs two types of self-dual supergravity theories in 2+2 dimensions, one based on curvature self-duality and the other involving torsionful curvature with an antisymmetric tensor field, each leading to specific equations of motion.

Contribution

It introduces novel self-dual supergravity models in 2+2 dimensions, connecting curvature self-duality with torsionful curvature and associated actions.

Findings

One model involves self-duality of Riemann curvature leading to Einstein-like equations.

The other involves torsionful curvature with an antisymmetric tensor, resulting in R^2-type equations.

Both models establish new links between self-duality conditions and supergravity dynamics.

Abstract

Starting from the new minimal multiplet of supergravity in $2+2$ dimensions, we construct two types of self-dual supergravity theories. One of them involves a self-duality condition on the Riemann curvature and implies the equations of motion following from the Hilbert-Einstein type supergravity action. The other one involves a self-duality condition on a {\it torsionful} Riemann curvature with the torsion given by the field-strength of an antisymmetric tensor field, and implies the equations of motion that follow from an $R^2$-type action.