Berlin 2005 – scientific programme

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GR: Gravitation und Relativitätstheorie

GR 7: Einstein-Yang-Mills-Higgs

GR 7.1: Talk

Friday, March 4, 2005, 18:15–18:30, TU BH262

Platonic Sphalerons in the Presence of a Dilaton Field — •Kari Myklevoll, Burkhard Kleihaus, and Jutta Kunz — Universität Oldenburg

When gravity is coupled to non-Abelian gauge theories a number of interesting phenomena arise, such as gravitationally bound monopoles. Since the coupling of gravity to Yang-Mills or Yang-Mills-Higgs theory has a very similar effect concerning the existence of classical solutions as the coupling to a scalar dilaton, we construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs-dilaton theory. We consider this study as a first step to obtain self-gravitating objects with only discrete symmetries. Related to rational maps of degree N, these platonic sphalerons can be assigned a Chern-Simons number Q=N/2. We present sphaleron solutions with degree N=1−4, possessing spherical, axial, tetrahedral and cubic symmetry. For all these sphalerons two branches of solutions exist, which bifurcate at a maximal value of the dilaton coupling constant.