The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System

Abstract

We use canonically-twisted modules for a certain super vertex operator algebra to construct the umbral moonshine module for the unique Niemeier lattice that coincides with its root sublattice. In particular, we give explicit expressions for the vector-valued mock modular forms attached to automorphisms of this lattice by umbral moonshine. We also characterize the vector-valued mock modular forms arising, in which four of Ramanujan's fifth order mock theta functions appear as components.

39 pages

References in corpus (2)

• Notes on the K3 Surface and the Mathieu group M_24
• Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

Cited by in corpus (5)

• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
• Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras
• Quasimodular moonshine and arithmetic connections