WZW action in odd dimensional gauge theories

TL;DR

This paper demonstrates the construction of WZW actions in odd-dimensional gauge theories using Wilson lines and loops, revealing their anomalous properties and potential for generalizing gauge theories in odd dimensions.

Contribution

It introduces a novel method to construct WZW actions in odd dimensions via Wilson lines and loops, including their gauge anomalies and boundary effects.

Findings

WZW actions can be constructed in odd dimensions using Wilson lines and loops.

These actions exhibit anomalous gauge and chiral transformations.

The approach allows generalization of gauge theories in odd-dimensional space-times.

Abstract

It is shown that Wess-Zumino-Witten (WZW) type actions can be constructed in odd dimensional space-times using Wilson line or Wilson loop. WZW action constructed using Wilson line gives anomalous gauge variations and the WZW action constructed using Wilson loop gives anomalous chiral transformation. We show that pure gauge theory including Yang-Mills action, Chern-Simons action and the WZW action can be defined in odd dimensional space-times with even dimensional boundaries. Examples in 3D and 5D are given. We emphasize that this offers a way to generalize gauge theory in odd dimensions. The WZW action constructed using Wilson line can not be considered as action localized on boundary space-times since it can give anomalous gauge transformations on separated boundaries. We try to show that such WZW action can be obtained in the effective theory when making localized chiral fermions decouple.