Importance of boundary conditions for topological production of textures and Skyrmions

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Abstract
The Kibble mechanism has recently been used to estimate the production of topological objects such as Skyrmions in hadronic events and textures in the context of the Universe. These objects correspond to a nontrivial third homotopy group of an appropriate group manifold. We discuss the importance of boundary conditions required for a topological description of such objects. These considerations show that textures do not have any topological meaning in the context of a homogeneous and isotropic universe and actually are homotopic to trivial configurations (as long as the universe is much bigger than the horizon size). We point out (and as has been noted by others) that a scale-invariant distribution of density fluctuations is expected for the spontaneous breaking of any global symmetry as long as the connected component of the vacuum manifold is degenerate. It does not matter whether the vacuum manifold has any nontrivial homotopy group. For the case of Skyrmion production in hadronic events, our considerations lead to a strong suppression of the Skyrmion production. A recent numerical simulation of the texture formation found that textures rarely occur. Our results provide a simple explanation of this result.

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