Anomalies in field theories with extra dimensions

TL;DR

The paper provides a pedagogical review of perturbative and non-perturbative anomalies in higher-dimensional field theories, with a focus on orbifold compactifications and extra dimensions. It develops and applies Fujikawa’s measure-based approach, employs Stora–Zumino descent to relate chiral, gauge, and gravitational anomalies, and surveys the Green–Schwarz and Wess–Zumino mechanisms for anomaly cancellation, including localized and bulk realizations on orbifolds. It also addresses regulator dependence of localized anomalies, the role of discrete Wilson lines, and the extension to higher-dimensional and string-derived orbifold models, as well as global and parity anomalies. The review highlights how consistent anomaly cancellation constrains model-building in extra-dimensional theories and clarifies the interplay between UV completions and low-energy effective descriptions.

Abstract

We give an overview of the issue of anomalies in field theories with extra dimensions. We start by reviewing in a pedagogical way the computation of the standard perturbative gauge and gravitational anomalies on non-compact spaces, using Fujikawa's approach and functional integral methods, and discuss the available mechanisms for their cancellation. We then generalize these analyses to the case of orbifold field theories with compact internal dimensions, emphasizing the new aspects related to the presence of orbifold singularities and discrete Wilson lines, and the new cancellation mechanisms that are becoming available. We conclude with a very brief discussion on global and parity anomalies.