Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism

Details Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism

1999-03-03

arxiv.org/abs/hep-lat/9903008v1

JHEP 9910 (1999) 002

Physics

High Energy Physics

High Energy Physics - Lattice

32 pages, LaTeX, 9 eps figures

Scientific paper

10.1088/1126-6708/1999/10/002

We point out that a fermion determinant of a chiral gauge theory on a 2D torus has a phase ambiguity proportional to the Polyakov loops along the boundaries, which can be reproduced by the overlap formalism. We show that the requirement on the fermion determinant that a singularity in the gauge field can be absorbed by a change of the boundary condition for the fermions, is not compatible with translational invariance in general. As a consequence, the gauge anomaly for singular gauge transformations discovered by Narayanan-Neuberger actually exists in any 2D U(1) chiral gauge theory unless the theory is vector-like. We argue that the gauge anomaly is peculiar to the overlap formalism with the Wigner-Brillouin phase choice and that it is not necessarily a property required in the continuum. We also generalize our results to any even dimension.

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