The exact decomposition of gauge variables in lattice Yang-Mills theory

TL;DR

This paper provides an exact, general decomposition of gauge variables in lattice SU(N) Yang-Mills theory, extending previous SU(2) and SU(3) results to arbitrary N, with implications for understanding gauge field structures.

Contribution

It introduces a set of defining equations for gauge link variable decomposition in lattice SU(N) Yang-Mills theory and solves them exactly, generalizing prior specific cases.

Findings

Derived the general form of gauge variable decomposition for SU(N).

Confirmed previous SU(2) and SU(3) results as special cases.

Provided a framework for exact lattice gauge field analysis.

Abstract

In this paper, we consider lattice versions of the decomposition of the Yang- Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2) and SU(3). As a result, we obtain the general form of the decomposition for SU(N) gauge link variables and confirm the previous results obtained for SU(2) and SU(3).