Wednesday, July 3, 2013

1307.0211 (Fabrizio Canfora)

Non-linear superposition law and Skyrme crystals    [PDF]

Fabrizio Canfora
Exact configurations of the four-dimensional Skyrme model are presented. The static configurations wind in a nontrivial way around the torus cycles while the profile behaves as a kink and saturates exactly a BPS bound. Furthermore, a class of exact time periodic Skyrmions is discovered. Within such class, it is possible to disclose a remarkable phenomenon which is a genuine effect of the Skyrme term. For a special value of the frequency the Skyrmions admit a non-linear superposition principle. One can combine two or more exact elementary Skyrmions (which may depend in a nontrivial way on all the spacelike coordinates) into a new exact composite Skyrmion. Due to such superposition law, despite the explicit presence of non linear effects in the energy momentum tensor, the interaction energy between the elementary Skyrmions can be computed exactly. The relations with the appearance of Skyrme crystals and plateau is discussed.
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