The Wess-Zumino-Witten term in non-commutative two-dimensional fermion models

TL;DR

This paper investigates the effective action in two-dimensional non-commutative fermion models, revealing that a Wess-Zumino-Witten like term emerges even in U(1) theories, derived from the axial anomaly.

Contribution

It demonstrates the appearance of a Wess-Zumino-Witten like term in non-commutative 2D fermion models, extending understanding of anomalies in such theories.

Findings

Wess-Zumino-Witten like term appears in U(1) non-commutative models

Effective action derived from axial anomaly

Extension of anomaly analysis to non-commutative geometry

Abstract

We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a Wess-Zumino-Witten like term arises.