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

Abstract

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.

32 pages, LaTeX, 9 eps figures

References in corpus (3)

• Overlap in odd dimensions
• Monte Carlo evaluation of a fermion number violating observable in 2D
• Overlap formula for the chiral multiplet

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• Lattice chirality and the decoupling of mirror fermions
• CPT anomaly in two-dimensional chiral U(1) gauge theories
• Torsion, topology and CPT anomaly in two-dimensional chiral U(1) gauge theory