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

Abstract

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.

30 pages

References in corpus (10)

• A construction of lattice chiral gauge theories
• Chiral Determinant as an Overlap of Two Vacua
• Chiral Fermions on the Lattice
• Chiral Fermions on the Lattice
• On the overlap formulation of chiral gauge theory
• A simulation of the Schwinger model in the overlap formalism
• Two dimensional twisted chiral fermions on the lattice
• Fractons in Twisted Multiflavor Schwinger Model
• Gravitational Lorentz anomaly from the overlap formula in 2-dimensions
• Determinant of twisted chiral Dirac Operator on the Lattice

Cited by in corpus (23)

• Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions
• Overlap in odd dimensions
• Gap Domain Wall Fermions
• Lattice Chiral Gauge Theories
• Finite size corrections in two dimensional gauge theories and a quantitative chiral test of the overlap
• Exact Chiral Symmetry on the Lattice
• Chiral fermions on the lattice
• Noncompact chiral U(1) gauge theories on the lattice
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Global obstructions to gauge-invariance in chiral gauge theory on the lattice
• Overlap formula for the chiral multiplet
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
• A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
• Renormalizability of a lattice chiral fermion in the overlap formulation
• Six-dimensional regularization of chiral gauge theories
• Weak coupling expansion of a chiral gauge theory on a lattice in the overlap formulation
• A numerical solution to the local cohomology problem in U(1) chiral gauge theories
• Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture
• Chiral Schwinger models without gauge anomalies