Anomalous Gauge Theories with Antisymmetric Tensor Fields

TL;DR

This paper develops dual formulations of anomalous U(1) gauge theories with antisymmetric tensor fields, revealing the roles of BF terms in anomaly cancellation and mass generation across four and six dimensions.

Contribution

It introduces dual descriptions of anomalous gauge theories using antisymmetric tensor fields and explores their implications for anomaly cancellation and mass terms.

Findings

BF terms can replace WZ and mass terms in dual theories.

Duality transformations are valid at classical and quantum levels.

BF terms are crucial for anomaly cancellation in non-abelian theories.

Abstract

We derive a dual theory of the four-dimensional anomalous U(1) gauge theory with a Wess--Zumino (WZ) term and with a St\"uckelberg type mass term by means of a duality transformation at each of the classical and quantum levels. It is shown that in the dual anomalous U(1) gauge theory, the $BF$ term with a rank-two antisymmetric tensor field plays the roles of the WZ term as well as the mass term of the U(1) gauge field. Similar anomalous U(1) gauge theory with $BF$ term is considered in six-dimensions by introducing a rank-four antisymmetric tensor field. In addition to this theory, we propose a six-dimensional anomalous U(1) gauge theory including an extended $BF$ term with a rank-two antisymmetric tensor field, discussing a difference between the two theories. We also consider a four-dimensional anomalous SU(2)$\times$U(1) gauge theory with $BF$ term and recognize a crucial role of the $BF$ term in cancelling the non-abelian chiral anomaly.