High Energy Physics

The elliptic genus of K3 and its decomposition into characters of the N=4 superconformal algebra of associated conformal field theories can be viewed as the outset of Mathieu Moonshine. Thus, extended supersymmetry induces additional properties of the elliptic genus, which so far lack a satisfactory geometric interpretation. We investigate the implications of this decomposition on geometric structures that underlie the elliptic genus.

We consider dual pairs of four dimensional heterotic/type IIA CHL models with 16 space-time supersymmetries. We provide strong evidence for the existence of an S-duality acting on the heterotic axion-dilaton by a Fricke involution S --> -1/NS, where N is the order of the orbifold symmetry. While most models are self-dual, in some cases S-duality relates the CHL model to a compactification of type IIA on an orbifold of T^6. We provide a simple criterion to determine whether a model is self-dual or not. Finally, we argue that in self-dual CHL models the lattices of electric and magnetic charges must be N-modular and verify this prediction.

Umbral moonshine attaches mock modular forms and meromorphic Jacobi forms to automorphisms of the Niemeier lattices. It is now known that this association can be recovered from specific, graded modules for the Niemeier lattice automorphism groups. We will describe recent progress in a program to realize these modules explicitly.

It has become a platitute to say that black holes are fascinating objects—but they really are, in part because they challenge our understanding of the fundamental reversibility of physical processes.

In the first part of the talk, I will review some of the classical ways black holes behave as dissipative systems, such as the "hair loss” phenomenon and the monotonic growth of horizon area. In the second part, I will explain how quantum mechanics (more precisely, the coupling of black holes to the quantum vacuum) affects the classical picture at late times, notably through particle creation and evaporation. I will argue that techniques from two-dimensional field theory can help bring clarity to the associated “information loss”

problem, and perhaps also point to new, unexpected predictions. My approach will be as model-independent as possible; that is, rather than investigating a particular scenario for black hole evaporation, I will aim to derive generic consequences from basic assumptions regarding the reversibility of black hole evaporation.