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

The CPT anomaly, which originally was found 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 a torus. The chiral determinant for periodic fermion fields changes sign under a CPT transformation of the background gauge field. Lorentz invariance also has an anomaly, which allows for the CPT theorem to be circumvented