Chiral Schwinger models without gauge anomalies

TL;DR

This paper introduces a broad class of two-dimensional Abelian quantum gauge models with massless fermions that avoid gauge anomalies despite having chiral asymmetry in their couplings, allowing explicit construction and solution.

Contribution

It presents a new class of chiral gauge models without gauge anomalies, providing explicit construction and solutions in the Hamiltonian framework.

Findings

Models with multiple photon fields and fermion flavors are constructed.

Conditions for anomaly cancellation are derived.

Models are explicitly solvable with manifest gauge and Lorentz invariance.

Abstract

We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian models in the Hamiltonian framework which can be constructed and solved by standard techniques. The general model describes $\Np$ photon fields and $\Nf$ flavors of Dirac fermions with $2\Nf\Np$ different coupling constants i.e. the chiral component of each fermion can be coupled to the gauge fields differently. We construct these models and find conditions so that no gauge anomaly appears. If these conditions hold it is possible to construct and solve the model explicitly, so that gauge- and Lorentz invariance are manifest.