Torsion, topology and CPT anomaly in two-dimensional chiral U(1) gauge theory

TL;DR

This paper investigates how spacetime torsion affects the CPT anomaly in two-dimensional chiral U(1) gauge theory, showing that torsion can shift the anomaly between different spin structures, with implications for higher dimensions.

Contribution

It demonstrates that spacetime torsion influences the CPT anomaly by altering spinor boundary conditions, allowing the anomaly to be relocated among spin structures in two-dimensional chiral gauge theories.

Findings

CPT anomaly depends on spin structure and torsion presence.

Torsion modifies boundary conditions of spinors.

Results extend to higher-dimensional theories.

Abstract

We consider the CPT anomaly of two-dimensional chiral U(1) gauge theory on a torus with topologically nontrivial zweibeins corresponding to the presence of spacetime torsion. The resulting chiral determinant can be expressed in terms of the standard chiral determinant without torsion, but with modified spinor boundary conditions. This implies that the two-dimensional CPT anomaly can be moved from one spin structure to another by choosing appropriate zweibeins. Similar results apply to higher-dimensional chiral gauge theories.