Gauge invariant topological interactions, such as the $D=5$ Chern-Simons (CS) term, 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 Kaluza-Klein (KK)-mode parity to the parity of space-time, leaving a single parity symmetry. It leads to new processes among KK modes e.g., the decay of a KK mode to a 2-body final state of KK modes. A formalism for the effective interaction among 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.

• Received 20 January 2006

DOI:https://doi.org/10.1103/PhysRevD.73.085001