  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.
