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arXiv · hep-th/9804070

Anomalous Gauge Theories with Antisymmetric Tensor Fields

Shinichi Deguchi·Tomoaki Mukai·Tadahito Nakajima
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Abstract

We derive a dual theory of the four-dimensional anomalous U(1) gauge theory with a Wess--Zumino (WZ) term and with a Stückelberg 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.

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Shinichi Deguchi, Tomoaki Mukai, Tadahito Nakajima. 1998-04-09. Anomalous Gauge Theories with Antisymmetric Tensor Fields. https://doi.org/10.1103/physrevd.59.065003

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