The Diaconescu-Moore-Witten anomaly and topological modular forms with level structure

by Arun Debray (Kentucky)

Thursday 24 Apr 2025, 16:15 → 17:15 Europe/Berlin

Geomatikum

Diaconescu-Moore-Witten (DMW) discovered an anomaly in type IIA string theory, which one can interpret as a constraint on the topology of spacetime for this theory and its compactifications. In order to calculate anomalies of these theories, one computes bordism groups of manifolds subject to DMW's constraint, which can be difficult. In this talk, I will review this story, then discuss work joint with Matthew Yu in which we approximate DMW's constraint with something called a "string^h structure." This approximation substantially simplifies the bordism computations, and in many situations suffices to determine the anomaly theory of a IIA compactification. I will also discuss a connection between string^h structures and topological modular forms with level structure, which is an essential part of our comptuations.