Topological modular forms and the absence of all heterotic global anomalies

Understand

We reformulate the question of the absence of global anomalies of heterotic string theory mathematically in terms of a certain natural transformation $\mathrm{TMF}^\bullet\to (I_{\mathbb{Z}}\Omega^\text{string})^{\bullet-20}$, from topological modular forms to the Anderson dual of string bordism groups, using the Segal-Stolz-Teichner conjecture.

• We will show that this natural transformation vanishes, implying that heterotic global anomalies are always absent.
• The fact that $\mathrm{TMF}^{21}(\mathrm{pt})=0$ plays an important role in the process.
• Along the way, we also discuss how the twists of $\mathrm{TMF}$ can be described under the Segal-Stolz-Teichner conjecture, by using the result of Freed and Hopkins concerning anomalies of quantum field theories.