  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.
