CPT anomaly in two-dimensional chiral U(1) gauge theories

TL;DR

This paper demonstrates the presence of a CPT anomaly in two-dimensional chiral U(1) gauge theories, showing that the chiral determinant changes sign under CPT, indicating a Lorentz invariance anomaly that bypasses the CPT theorem.

Contribution

It provides an exact result showing the CPT anomaly in 2D chiral U(1) gauge theories, extending the understanding of anomalies beyond perturbation theory.

Findings

CPT anomaly exists in 2D chiral U(1) gauge theories

Chiral determinant changes sign under CPT transformation

Lorentz invariance anomaly allows CPT theorem to be circumvented

Abstract

The CPT anomaly, which was first seen in perturbation theory for certain four-dimensional chiral gauge theories, is also present in the exact result for a class of two-dimensional chiral U(1) gauge theories on the torus. Specifically, the chiral determinant for periodic fermion fields changes sign under a CPT transformation of the background gauge field. There is, in fact, an anomaly of Lorentz invariance, which allows for the CPT theorem to be circumvented.