Infinitely many conservation laws in self-dual Yang--Mills theory

TL;DR

This paper introduces a novel family of infinitely many conserved currents in the self-dual sector of SU(2) Yang-Mills theory, derived through a nonlocal field transformation and generalized integrability concepts, applicable across various space-time dimensions.

Contribution

It presents a new method to generate infinitely many conserved currents in self-dual Yang-Mills theory using a nonlocal decomposition and integrability ideas, extending to arbitrary dimensions.

Findings

Derived a new family of conserved currents in self-dual SU(2) Yang-Mills theory.

The currents are related to area-preserving diffeomorphisms on the reduced target space.

Method is covariant and applicable in any space-time dimension with arbitrary signature.

Abstract

Using a nonlocal field transformation for the gauge field known as Cho--Faddeev--Niemi--Shabanov decomposition as well as ideas taken from generalized integrability, we derive a new family of infinitely many conserved currents in the self-dual sector of SU(2) Yang-Mills theory. These currents may be related to the area preserving diffeomorphisms on the reduced target space. The calculations are performed in a completely covariant manner and, therefore, can be applied to the self-dual equations in any space-time dimension with arbitrary signature.