An effective action for monopoles and knot solitons in Yang-Mills theory

TL;DR

This paper develops an effective action framework for monopoles and knot solitons in Yang-Mills theory, connecting lattice results with continuum descriptions and extending to SU(N) cases.

Contribution

It introduces a method to derive an effective action for coset fields in Yang-Mills theory, highlighting the role of knot solitons and monopoles, and extends the approach to SU(N).

Findings

Effective action for coset fields in Yang-Mills theory.

Knot solitons as physical excitations.

Relation between large N limit and monopole dominance.

Abstract

By comparision with numerical results in the maximal Abelian projection of lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the coset space SU(2)/U(1). The Yang-Mills connection is parameterized in a special way to separate the dependence on the coset field. The coset field is then regarded as a collective variable, and a method to obtain its effective action is developed. It is argued that the physical excitations of the effective action may be knot solitons. A procedure to calculate the mass scale of knot solitons is discussed for lattice gauge theories in the maximal Abelian projection. The approach is extended to the SU(N) Yang-Mills theory. A relation between the large N limit and the monopole dominance is pointed out.