K3 String Theory, Lattices and Moonshine

Understand

In this paper we address the following two closely related questions.

• First, we complete the classification of finite symmetry groups of type IIA string theory on $K3\times \mathbb R^6$, where Niemeier lattices play an important role.
• This extends earlier results by including points in the moduli space with enhanced gauge symmetries in spacetime, or, equivalently, where the world-sheet CFT becomes singular.
• After classifying the symmetries as abstract groups, we study how they act on the BPS states of the theory.