Partial duality in SU(N) Yang-Mills theory

TL;DR

This paper extends a set of variables for describing the infrared behavior of SU(2) Yang-Mills theory to SU(N), revealing a decomposition of the connection and relating curvature to symplectic forms, proposing models for stable topological solitons.

Contribution

It generalizes variables for infrared SU(2) Yang-Mills to SU(N), connecting the connection decomposition to irreducible representations and symplectic forms, and introduces nonlinear chiral models for topological solitons.

Findings

Decomposition of SU(N) connection via SO(N-1) representations

Relation of curvature to symplectic Kirillov forms

Proposal of nonlinear chiral models for stable solitons

Abstract

Recently we have proposed a set of variables for describing the infrared limit of four dimensional SU(2) Yang-Mills theory. here we extend these variables to the general case of four dimensional SU(N) Yang-Mills theory. We find that the SU(N) connection A decomposes according to irreducible representations of SO(N-1) and the curvature two-form F is related to the symplectic Kirillov two forms that characterize irreducible representations of SU(N). We propose a general class of nonlinear chiral models that may describe stable, soliton-like configurations with nontrivial topological numbers.