Topological modularity of supermoonshine What is an elliptic object? What is an elliptic object? Elliptic Cohomology Global Anomalies in String Theory
Jan Albert (C. N. Yang Institute for Theoretical Physics, Stony Brook University, , , Stony Brook, NY 11794-3840, , , USA, Simons Center for Geometry and Physics, Stony Brook University, , , Stony Brook, NY 11794-3636, , , USA); Justin Kaidi (Simons Center for Geometry and Physics, Stony Brook University, , , Stony Brook, NY 11794-3636, , , USA, Department of Physics, University of Washington, , , Seattle, WA 98195, , , USA, Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, , , Kashiwa, Chiba 277-8583, , , Japan); Ying-Hsuan Lin (Jefferson Physical Laboratory, Harvard University, , , Cambridge, MA 02138, , , USA)
Abstract The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory’s gravitational anomaly. In this note we verify this prediction in Duncan’s supermoonshine module, as well as in tensor products and orbifolds thereof. Along the way we develop machinery for computing the elliptic genera of general alternating orbifolds and discuss the relation of this construction to the elusive “periodicity class” of TMF.