Mathematical and Theoretical Physics Seminar: "Moonshine in Spacetime: Automorphy, Algebras, and String Compactifications"
(sign-up)Natalie Paquette, Caltech
Physics and Mathematics
New examples of moonshine--- relationships between finite groups and special classes of (mock) modular forms--- have been proliferating in recent years, starting with the discovery of a Mathieu group moonshine apparently connected to conformal field theory (CFT) on the K3 surface. While many aspects of these new moonshines remain mysterious, in this talk we will stress the power of spacetime string theory---as opposed to worldsheet string theory or CFT---to shine light on some of moonshine's mysteries. We will exhibit this in two vignettes. In part 1, we give a conceptual, physical explanation of the genus zero property of Monstrous moonshine using properties of a heterotic string compactification, concomitantly placing algebraic aspects of Borcherds' proof, such as the Monstrous Lie algebra, in a physical context. This gives a precise instantiation of the role of Generalized Kac-Moody algebras organizing BPS states in string theory, as first suggested by Harvey and Moore. In part 2, we completely determine a class of elliptic genera encoding the possible symmetries acting on BPS states in K3 CFT using wall-crossing properties of spacetime BPS states on K3 x T2 and orbifolds thereof. These in turn produce a class of 1/4-BPS counting functions in spacetime. The latter are Siegel automorphic forms that constitute predictions for the reduced Gromov-Witten theory of orbifolds of K3 x T2 and account for the entropy of supersymmetric black holes.
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