Anomaly cancellation in M-theory: a critical review

TL;DR

This paper provides a detailed review of anomaly cancellation mechanisms in M-theory, focusing on 5-brane and S^1/Z_2 anomalies, emphasizing the importance of correct coefficients, signs, and a necessary modification to the Chern-Simons term.

Contribution

It offers a reanalysis of anomaly cancellation in M-theory, revealing a previously overlooked factor that necessitates a modification of the Chern-Simons term for consistent anomaly cancellation.

Findings

Identification of a neglected factor affecting anomaly cancellation

Modification of the Chern-Simons term for local anomaly cancellation

Ensuring consistent anomaly cancellation on S^1/Z_2 with periodicity

Abstract

We carefully review the basic examples of anomaly cancellation in M-theory: the 5-brane anomalies and the anomalies on S^1/Z_2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly fix all coefficients and signs, proper attention is paid to issues of orientation, chirality and the Euclidean continuation. Independent of the conventions chosen, the Chern-Simons and Green-Schwarz terms must always have the same sign. The reanalysis of the reduction to the heterotic string on S^1/Z_2 yields a surprise: a previously neglected factor forces us to slightly modify the Chern-Simons term, similar to what is needed for cancelling the normal bundle anomaly of the 5-brane. This modification leads to a local cancellation of the anomaly, while maintaining the periodicity on S^1.