Self-dual gravity and the chiral model

TL;DR

This paper demonstrates the equivalence between the self-dual Einstein equations and a two-dimensional chiral model, providing new insights and formulations for understanding self-dual gravity through integrable systems.

Contribution

It establishes a novel connection between self-dual gravity and the chiral model, including an analog of Plebanski equations and a Hamiltonian formulation.

Findings

Equivalence between SDE and the chiral model established

Provides a new Hamiltonian formulation for SDE

Introduces an analog of Plebanski equations for self-dual metrics

Abstract

The self-dual Einstein equation (SDE) is shown to be equivalent to the two dimensional chiral model, with gauge group chosen as the group of area preserving diffeomorphisms of a two dimensional surface. The approach given here leads to an analog of the Plebanski equations for general self-dual metrics, and to a natural Hamiltonian formulation of the SDE, namely that of the chiral model.