Chern-Simons and WZW Anomaly Cancelations Across Dimensions

TL;DR

This paper demonstrates how the WZW functional in four dimensions can be derived from five-dimensional Chern-Simons theory, illustrating anomaly cancellation in boundary-bulk gauge systems with a simple U(1) model.

Contribution

It provides a clear derivation of the 4D WZW functional from 5D Chern-Simons theory and shows anomaly cancellation in a boundary-bulk gauge system.

Findings

WZW functional derived from Chern-Simons in 5D

Anomaly cancellation between CS and WZW terms

Pedagogical U(1) gauge model illustration

Abstract

The WZW functional in D=4 can be derived directly from the Chern-Simons functional of a compactified D=5 gauge theory and the boundary fermions it supplants. A simple pedagogical model based on U(1) gauge groups illustrates how this works. A bulk-boundary system with the fermions eliminated manifestly evinces anomaly cancelations between CS and WZW terms.