Anomalies, Chern-Simons Terms and Chiral Delocalization in Extra Dimensions

TL;DR

This paper explores the role of Chern-Simons terms in extra-dimensional models, revealing their impact on anomaly cancellation, KK-mode interactions, and chiral symmetry, with implications for observable physical processes.

Contribution

It develops a formalism for effective KK-mode interactions, analyzes KK-mode decays, and connects higher-dimensional gauge theories to 4D chiral Lagrangians and anomaly structures.

Findings

Chern-Simons terms ensure anomaly cancellation in extra dimensions.

KK-mode parity is linked to space-time parity, affecting decay processes.

A formalism for KK-mode interactions and anomalies is established.

Abstract

Gauge invariant topological interactions, such as the D=5 Chern-Simons terms, are required in models in extra dimensions that split anomaly free representations. The Chern-Simons term is necessary to maintain the overall anomaly cancellations of the theory, but it can have significant, observable, physical effects. The CS-term locks the KK-mode parity to the parity of space-time, leaving a single parity symmetry. It leads to new processes amongst KK-modes, eg, the decay of a KK-mode to a 2-body final state of KK-modes. A formalism for the effective interaction amongst KK-modes is constructed, and the decay of a KK-mode to KK-mode plus zero mode is analyzed as an example. We elaborate the general KK-mode current and anomaly structure of these theories. This includes a detailed study of the triangle diagrams and the associated ``consistent anomalies'' for Weyl spinors on the boundary branes. We also develop the non-abelian formalism. We illustrate this by showing in a simple way how a D=5 Yang-Mills ``quark flavor'' symmetry leads to the D=4 chiral lagrangian of mesons and the quantized Wess-Zumino-Witten term.