$\ast$-SDYM fields and heavenly spaces: II. Reductions of the $\ast$-SDYM system

TL;DR

This paper explores reductions of the self-dual Yang-Mills system with $igast$-bracket Lie algebra, connecting it to heavenly equations and demonstrating how sequences of $su(N)$ fields approach curved heavenly spaces as $N$ increases.

Contribution

It introduces new reductions of the $igast$-SDYM system to heavenly equations and constructs a sequence of $su(N)$ fields converging to curved heavenly spaces.

Findings

Reductions of $igast$-SDYM to Husain-Park heavenly equation.

Connection between $sl(N,{oldmath{$C$})$ SDYM and heavenly spaces.

Sequence of $su(N)$ fields tending to curved heavenly space as $N o abla$.

Abstract

Reductions of self-dual Yang-Mills (SDYM) system for $\ast$-bracket Lie algebra to the Husain-Park (HP) heavenly equation and to $sl(N,{\boldmath{$C$})$ SDYM equation are given. An example of a sequence of $su(N)$ chiral fields ($N\geq 2$) tending for $N\to\infty$ to a curved heavenly space is found.