Topological modular forms and heretoric string theory

09/29/2023 2:00 pm - 3:00 pm
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA
Special Seminar

Speaker: Mayuko Yamashita, Kyoto University

Title: Topological modular forms and heretoric string theory

Abstract: 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 (, we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF.

Furthermore, we have a recent update ( 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.