1999/03/03 by Taku Izubuchi, Jun Nishimura · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #High-Energy Particle Collisions Research #Quantum Chromodynamics and Particle Interactions #hep-lat
paper · pdf · doi:10.1088/1126-6708/1999/10/002
published as JHEP 9910 (1999) 002 · 32 pages, LaTeX, 9 eps figures
arxiv created 1999/03/03 · openalex publication_date 1999/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.