Anomaly free U(1) chiral gauge theories on a two dimensional torus

Details Anomaly free U(1) chiral gauge theories on a two dimensional torus Anomaly free U(1) chiral gauge theories on a two dimensional torus

1996-03-29

arxiv.org/abs/hep-th/9603204v1

Nucl.Phys. B477 (1996) 521-548

Physics

High Energy Physics

High Energy Physics - Theory

30 pages

Scientific paper

10.1016/0550-3213(96)00405-1

We consider anomaly free combinations of chiral fermions coupled to $U(1)$ gauge fields on a 2D torus first in the continuum and then on the lattice in the overlap formulation. Both in the continuum and on the lattice, when the background consists of sufficiently large constant gauge potentials the action induced by the fermions varies significantly under certain singular gauge transformations. ``Ruling away'' such discontinuities cannot be justified in the continuum framework and does not naturally fit on the lattice. Complete gauge invariance in the continuum can be restored in some models by choosing special boundary conditions for the fermions. Evidence is presented that gauge averaging the overlap phases in these models produces correct continuum results.

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