K3 String Theory, Lattices and Moonshine

Abstract

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. In particular, we classify the conjugacy classes in the T-duality group $O^{+}({\Gamma }^{4,20})$ which represent physically distinct symmetries. Subsequently, we make two conjectures regarding the connection between the corresponding twining genera of $K3$ CFTs and Conway and umbral moonshine, building upon earlier work on the relation between moonshine and the $K3$ elliptic genus.

46 pages, Magma code included as ancillary file. V2: references adjusted

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Cited by in corpus (5)

• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
• Conway Subgroup Symmetric Compactifications Of Heterotic String
• Umbral Moonshine and String Duality
• TASI Lectures on Moonshine