On Infinite-Dimensional Algebras of Symmetries of the Self-Dual Yang-Mills Equations

TL;DR

This paper explores the infinite-dimensional symmetry algebras of the self-dual Yang-Mills equations, revealing their structure through twistor theory and extending conformal symmetries.

Contribution

It introduces a current-type algebra of symmetries and an affine extension of conformal symmetries using twistor methods, providing new insights into their structure.

Findings

Extended conformal symmetries have a simple twistor-based description.

A current-type algebra of symmetries is constructed.

The affine extension of conformal symmetries is discussed.

Abstract

Infinite-dimensional algebras of hidden symmetries of the self-dual Yang-Mills equations are considered. A current-type algebra of symmetries and an affine extension of conformal symmetries introduced recently are discussed using the twistor picture. It is shown that the extended conformal symmetries of the self-dual Yang-Mills equations have a simple description in terms of Ward's twistor construction.