Gauge boson mass dependence and chiral anomalies in generalized massless Schwinger models

Abstract

I bosonize the position-space correlators of flavor-diagonal scalar fermion bilinears in arbitrary generalizations of the Schwinger model with nF massless fermions coupled to nA gauge bosons for nF ≥ nA. For nA = nF, the fermion bilinears can be bosonized in terms of nF scalars with masses proportional to the gauge couplings. As in the Schwinger model, bosonization can be used to find all correlators, including those that are forbidden in perturbation theory by anomalous chiral symmetries, but there are subtleties when there is more than one gauge boson. The new result here is the general treatment of the dependence on gauge boson masses in models with more than one gauge symmetry. For nA < nF, there are fermion bilinears with nontrivial anomalous dimensions and there are unbroken chiral symmetries so some correlators vanish while others are non-zero due to chiral anomlies. Taking careful account of the dependence on the masses, I show how the nA < nF models emerge from nA = nF as gauge couplings (and thus gauge boson masses) go to zero. When this is done properly, the limit of zero gauge coupling is smooth. Our consistent treatment of gauge boson masses guarantees that anomalous symmetries are broken while unbroken chiral symmetries are preserved because correlators that break the non-anomalous symmetries go to zero in the limit of zero gauge coupling.