A Master Equation for Multi-Dimensional Non-Linear Field Theories

TL;DR

This paper introduces a master equation framework for multi-dimensional non-linear field theories, unifying the understanding of integrable equations across various dimensions, including 2D and 4D cases.

Contribution

The paper presents a novel master equation that systematically unifies 2D integrable non-linear equations and 4D self-dual equations, extending to higher dimensions.

Findings

Provides a new systematic approach to multi-dimensional non-linear theories

Unifies 2D integrable and 4D self-dual equations under a single framework

Facilitates exploration of higher-dimensional generalizations

Abstract

A master equation ( $n$ dimensional non--Abelian current conservation law with mutually commuting current components ) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.