# Topological modular forms and heretoric string theory

### APA

Yamashita, M. (2023). Topological modular forms and heretoric string theory. Perimeter Institute. https://pirsa.org/23100074

### MLA

Yamashita, Mayuko. Topological modular forms and heretoric string theory. Perimeter Institute, Oct. 05, 2023, https://pirsa.org/23100074

### BibTex

@misc{ pirsa_PIRSA:23100074, doi = {10.48660/23100074}, url = {https://pirsa.org/23100074}, author = {Yamashita, Mayuko}, keywords = {Mathematical physics}, language = {en}, title = {Topological modular forms and heretoric string theory}, publisher = {Perimeter Institute}, year = {2023}, month = {oct}, note = {PIRSA:23100074 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

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Zoom link: https://pitp.zoom.us/j/95550331572?pwd=OW1oYlBvUWVxaGNJRWl5aHVrS0pJZz09