Cosmic String Helicity: Constraints on Loop Configurations, and the Quantization of Baryon Number

Abstract

We apply the concept of helicity from classical hydrodynamics to elucidate two problematical issues in cosmic string physics. Helicity, the space integral of the scalar product of a velocity-like field with its vorticity field (curl), can be defined for a complex scalar field in analogy with fluids. We dwell on the topological interpretation of helicity as related to the linking of field lines of the vorticity field. Earlier works failed to fully implement this interpretation for cosmic strings by missing a term connected with the linking of these lines inside the strings. As a result paradoxical conclusions were drawn: global cosmic string loops may not take on certain simple shapes, and baryon number is not quantized in integers in the presence of local cosmic strings in gauge theory. We show that both paradoxes are removed when internal contributions to helicity are properly taken into account. In particular, quantization of baryon number can be understood within a special case of the Glashow-Weinberg-Salam model if cosmic strings are the unique mechanism for baryosynthesis. In addition, we find a new constraint on the permitted linkages of cosmic strings in a string tangle.