Description |
I will review the appearance of moonshines associated with the Mathieu Groups in the counting of BPS states in N=4 supersymmetric string theory. Moonshine refines the the second-quantised elllptic genus of K3 and implies a product formula to a closely related Siegel modular form. These Siegel modular forms in certain cases are related to Lie algebras whose root lattices emerge from the walls of marginal stabilty of quarter-BPS dyons. We argue for the existence of a new class of Lie algebras that arise for particular N=4 supersymmetric string theories. If time permits, I will discuss examples from Umbral moonshine that non-trivially extends Mathieu moonshine.
|