Anomalies in M-theory on singular G_2-manifolds

TL;DR

This paper addresses anomaly cancellation in M-theory compactified on G_2-manifolds with conical singularities, proposing a local mechanism to cancel gauge and gravitational anomalies at each singularity.

Contribution

It introduces a novel local anomaly cancellation mechanism for G_2-manifolds with conical singularities, extending previous global approaches.

Findings

Proposes a method to cancel anomalies locally at each singularity.

Demonstrates the cancellation involves field cut-offs near singularities.

Connects anomaly cancellation to a process similar to five-brane normal bundle anomaly cancellation.

Abstract

When M-theory is compactified on G_2-holonomy manifolds with conical singularities, charged chiral fermions are present and the low-energy four-dimensional theory is potentially anomalous. We reconsider the issue of anomaly cancellation, first studied by Witten. We propose a mechanism that provides local cancellation of all gauge and mixed gauge-gravitational anomalies, i.e. separately for each conical singularity. It is similar in spirit to the one used to cancel the normal bundle anomaly in the presence of five-branes. It involves smoothly cutting off all fields close to the conical singularities, resulting in an anomalous variation of the 3-form C and of the non-abelian gauge fields present if there are also ADE singularities.