Topological modular forms and heretoric string theory


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


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


          @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}}

Mayuko Yamashita Kyoto University


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.


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