Particle Theory Seminar: Greg Moore (Rutgers), Three Projects Using Lattices, Modular Forms, K3-Surfaces, And String Theory

Part 1 begins with a very brief review of Moonshine - old and new. I will then describe some special points (called CSS points) in the toroidal compactifications of heterotic strings with large (but finite) symmetry groups that are naturally subgroups of the Conway group. Then I will, regrettably, conclude that a conjectured M24 Moonshine property of refined Gromov-Witten invariants of K3 surfaces is actually not present. Part 2 will examine some applications of the CSS points in view of heterotic-typeII string duality. This will raise the question of the validity of a consistency condition for asymmetric orbifolds that has been used in string theory since 1987. I will argue that it has been misinterpreted. Part 3 briefly describes the computation of Zamolodchikov volumes of moduli spaces of 2d CFT’s associated to symmetric products of K3 surfaces, as well as the motivation for this computation from questions regarding AdS/CFT duality. The talk is modular in the sense that I can stop after part 1 or part 2,depending on the time and interest of the audience.