Topological modular forms and the absence of a heterotic global anomaly

TL;DR

This paper investigates the potential for a $bZ_{24}$-valued gravitational global anomaly in heterotic string compactifications to two dimensions, proposing that topological modular forms can demonstrate its absence under certain conjectures.

Contribution

It introduces a novel approach using topological modular forms to analyze and potentially prove the absence of a specific global anomaly in heterotic string theories.

Findings

The $bZ_{24}$ gravitational anomaly can be shown to vanish using topological modular forms.

The result depends on the validity of the Stolz-Teichner conjecture.

Provides a new perspective on anomaly cancellation in string theory.

Abstract

Spacetime theories obtained from perturbative string theory constructions are automatically free of perturbative anomalies, but it is not settled whether they are always free of global anomalies. Here we discuss a possible $\mathbb{Z}_{24}$-valued pure gravitational anomaly of heterotic compactifications down to two spacetime dimensions, and point out that it can be shown to vanish using the theory of topological modular forms, assuming the validity of the Stolz-Teichner conjecture.