Integrable subsystem of Yang--Mills dilaton theory

Details Integrable subsystem of Yang--Mills dilaton theory Integrable subsystem of Yang--Mills dilaton theory

2007-03-26

arxiv.org/abs/hep-th/0703224v3

J.Phys.A41:095401,2008

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, LaTex. Version 3: appendix added where the equivalence of the field equations for the full model and the submodel is

Scientific paper

10.1088/1751-8113/41/9/095401

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.

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