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

TL;DR

This paper extends the Abelian decomposition method to Sp(2N) Yang-Mills theory, revealing how the connection decomposes into irreducible SO(N) representations, aiding the understanding of its infrared behavior.

Contribution

It introduces a novel decomposition of Sp(2N) Yang-Mills connections based on SO(N) irreducible representations, generalizing previous work on SO(N).

Findings

Sp(2N) connection decomposes into SO(N) irreducible components

The method generalizes Abelian decomposition to a new class of gauge theories

Provides a framework for analyzing infrared limits of Sp(2N) Yang-Mills theory

Abstract

In the previous paper, we generalized the method of Abelian decomposition to the case of SO(N) Yang-Mills theory. This method that was proposed by Faddeev and Niemi introduces a set of variables for describing the infrared limit of a Yang-Mills theory. Here, we extend the decomposition method further to the general case of four-dimensional Sp(2N) Yang-Mills theory. We find that the Sp(2N) connection decomposes according to irreducible representations of SO(N).