A double complex construction and discrete Bogomolny equations

TL;DR

This paper introduces a novel discrete analog of the Bogomolny equations derived from self-dual Yang-Mills equations using a double complex construction, advancing discrete gauge theory models.

Contribution

It presents a new discrete formulation of Bogomolny equations based on a double complex approach, linking discrete self-dual equations to matrix-valued difference equations.

Findings

Derived a discrete Bogomolny system from self-dual equations.

Established a double complex framework for discretization.

Provided a new perspective on discrete gauge theories.

Abstract

We study discrete models which are generated by the self-dual Yang-Mills equations. Using a double complex construction we construct a new discrete analog of the Bogomolny equations. Discrete Bogomolny equations, a system of matrix valued difference equations, are obtained from discrete self-dual equations