Abelian Decomposition of SO(2N) Yang-Mills Theory

TL;DR

This paper extends the Abelian decomposition method, originally applied to SU(N), to SO(2N) Yang-Mills theory, revealing a new way to analyze low-energy soliton configurations and topological features.

Contribution

It generalizes the Abelian decomposition technique to SO(2N) gauge theories, providing a framework for understanding their low-energy topological structures.

Findings

Decomposition of SO(2N) connection into irreducible SO(N) representations

Expected description of soliton-like configurations in the low-energy limit

Discussion on generalization to SO(2N+1) Yang-Mills theory

Abstract

Faddeev and Niemi have proposed a decomposition of SU(N) Yang-Mills theory in terms of new variables, appropriate for describing the theory in the infrared limit. We extend this method to SO(2N) Yang-Mills theory. We find that the SO(2N) connection decomposes according to irreducible representations of SO(N). The low energy limit of the decomposed theory is expected to describe soliton-like configurations with nontrivial topological numbers. How the method of decomposition generalizes for $SO(2N+1)$ Yang-Mills theory is also discussed.