Axial and gauge anomalies in a theory with one and two-form gauge fields

TL;DR

This paper investigates axial and gauge anomalies in a theory with vector and tensor gauge fields coupled topologically, revealing the emergence of an anomalous axial current contrary to previous findings.

Contribution

It demonstrates that certain topological couplings between fermionic currents and tensor fields produce axial anomalies, challenging prior results in the literature.

Findings

Topological coupling induces axial anomaly

Contradicts previous results with tensor couplings

Highlights importance of coupling structure in anomalies

Abstract

We study the problem of axial and gauge anomalies in a reducible theory involving vector and tensor gauge fields coupled in a topological way. We consider that vector and axial fermionic currents couple with the tensor field in the same topological manner as the vector gauge one. This kind of coupling leads to an anomalous axial current, contrarily to the results found in literature involving other tensor couplings, where no anomaly is obtained.