Chirality and fermion number in a knotted soliton background

Details Chirality and fermion number in a knotted soliton background Chirality and fermion number in a knotted soliton background

2002-12-04

arxiv.org/abs/hep-th/0212053v1

Phys.Lett. B557 (2003) 121-124

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1016/S0370-2693(03)00200-4

We consider the coupling of a single Dirac fermion to the three component unit vector field which appears as an order parameter in the Faddeev model. Classically, the coupling is determined by requiring that it preserves a certain local frame independence. But quantum mechanically the separate left and right chiral fermion number currents suffer from a frame anomaly. We employ this anomaly to compute the fermion number of a knotted soliton. The result coincides with the self-linking number of the soliton. In particular, the anomaly structure of the fermions relates directly to the inherent chiral properties of the soliton. Our result suggests that interactions between fermions and knotted solitons can lead to phenomena akin the Callan-Rubakov effect.

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