Moyal Nahm Equations

TL;DR

This paper explores the properties and solutions of Nahm equations in 3 and 7 dimensions, focusing on algebraic structures, matrix representations, and the large N limit using Moyal brackets, leading to novel solutions.

Contribution

It introduces a new algebraic framework for 7-dimensional Nahm equations and constructs matrix representations, extending solutions via Moyal brackets in the large N limit.

Findings

Residues at poles form an algebra in 7D Nahm equations

Constructed a broad class of matrix representations of this algebra

Derived non-trivial solutions using Moyal brackets and Wigner functions

Abstract

Various aspects of the Nahm equations in 3 and 7 dimensions are investigated. The residues of the variables at simple poles in the 7-dimensional case form an algebra. A large class of matrix representations of this algebra is constructed. The large $N$ limit of these equations is taken by replacing the commutators by Moyal Brackets, and a set of non trivial solutions in a generalised form of Wigner distribution functions is obtained.