Anomalies in field theories with extra dimensions

TL;DR

This paper reviews anomalies in field theories with extra dimensions, covering their computation, cancellation mechanisms, and special considerations for orbifold compactifications and singularities.

Contribution

It provides a comprehensive overview of anomalies in higher-dimensional theories, including new cancellation methods related to orbifold singularities and Wilson lines.

Findings

Standard anomalies can be computed using Fujikawa's approach.

Orbifold singularities introduce new anomaly cancellation mechanisms.

Global and parity anomalies are briefly discussed.

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.