On the Moyal deformation of Nahm Equations in seven dimensions

TL;DR

This paper extends the Nahm equations in seven dimensions to the Weyl-Wigner-Moyal formalism, providing new solutions for SU(2) and SL(2,R) gauge groups, thus bridging classical and quantum formalisms in higher-dimensional gauge theories.

Contribution

It introduces a Moyal deformation of the Nahm equations in seven dimensions and explicitly constructs new solutions for specific gauge groups.

Findings

New solutions for SU(2) and SL(2,R) gauge groups

Demonstration of the Moyal deformation of Nahm equations

Extension of self-dual Yang-Mills equations to a quantum formalism

Abstract

We show how the reduced (anti-)self-dual Yang-Mills equations in seven dimensions described by the Nahm equations can be carried over to the Weyl-Wigner-Moyal formalism. In the process some new solutions for the cases of gauge groups SU(2) and SL(2,R) are explicitly obtained.