A global anomaly from the Z-string
arXiv:hep-th/9702023 · doi:10.1016/S0550-3213(97)00206-X
Abstract
The response of isodoublet fermions to classical backgrounds of essentially 2-dimensional boson fields in SU(2) Yang-Mills-Higgs theory is investigated. In particular, the spectral flow of Dirac eigenvalues is calculated for a non-contractible sphere of configurations passing through the vacuum and the Z-string (the embedded vortex solution). Also, a non-vanishing Berry phase is established for adiabatic transport "around" the Z-string. These results imply the existence of a new type of global (non-perturbative) gauge anomaly in SU(2) Yang-Mills-Higgs quantum field theory with a single doublet of left-handed fermions. Possible extensions to other chiral gauge field theories are also discussed.
In Section 6 error corrected for SU(2) theories with general isospin; conclusions changed significantly
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- Fermion zero-modes of a new constrained instanton in Yang-Mills-Higgs theory
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