Self-Duality in 3+3 Dimensions and the KP Equation

TL;DR

This paper explores generalized self-duality conditions in 3+3 dimensions and demonstrates how the KP equation can be derived from these conditions on specific gauge fields.

Contribution

It introduces a novel connection between self-duality in higher dimensions and integrable equations like the KP equation.

Findings

Derivation of the KP equation from self-duality conditions

Extension of self-duality concepts to paracomplex manifolds

Application to $SL(2,R)$ gauge fields

Abstract

We consider two types of generalized self-duality conditions for Yang-Mills fields on paracomplex manifolds of arbitrary dimension. We then specialize to $3+3$ dimensions and show how one can obtain the KP equation from these self-duality conditions on $SL(2,R)$ valued gauge fields.