Integrable subsystem of Yang--Mills dilaton theory

TL;DR

This paper identifies an integrable subsystem within SU(2) Yang-Mills dilaton theory using a specific decomposition, constructs static solutions, and explains their energy behavior through a Bogomolny bound.

Contribution

It introduces a new integrable subsystem of Yang-Mills dilaton theory, constructs its static solutions, and relates them to known numerical solutions with a Bogomolny bound.

Findings

Existence of infinitely many symmetries and conserved currents in the subsystem.

Construction of static solutions matching limiting cases of the full system.

Derivation of a Bogomolny bound explaining linear energy growth.

Abstract

With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many symmetries and infinitely many conserved currents. Further, we construct infinitely many static solutions of this integrable subsystem. These solutions can be identified with certain limiting solutions of the full system, which have been found previously in the context of numerical investigations of the Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the integrable subsystem and show that our static solutions are, in fact, Bogomolny solutions. This explains the linear growth of their energies with the topological charge, which has been observed previously. Finally, we discuss some generalisations.