Operator solutions of two-dimensional chiral gauge theories

TL;DR

This paper derives exact operator solutions for anomaly-free 2D chiral abelian gauge theories, revealing anomaly cancellation as a consistency condition and exploring fermion condensates and massive extensions.

Contribution

It provides the first explicit operator solutions for these theories and links anomaly cancellation to solution consistency, including massive fermion extensions.

Findings

Anomaly cancellation conditions emerge from solution consistency

Fermion condensates violate fermion-number conservation

Bosonised Lagrangian for massive theory verified with Gupta-Bleuler condition

Abstract

The exact operator solutions of two-dimensional anomaly-free chiral abelian gauge theories are obtained. We show that anomaly-cancellation conditions arise as consistency requirements of these solutions. For a certain class of flavour symmetries, fermion condensates are constructed. These are shown to violate the fermion-number conservation rule. The models are extended to include massive fermions. We propose a bosonised lagrangian for the massive theory and verify that it complies with the Gupta-Bleuler condition.