# 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.

## Key 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.