**Speaker: **Yuji Tachikawa (Kavli IPMU, U Tokyo)

**Title: **On the absence of global anomalies of heterotic string theories**Abstract:** Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.

In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.

The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.