The Moonshine Anomaly

Abstract

The anomaly for the Monster group $\mathbb{M}$ acting on its natural (aka moonshine) representation $V^{♮}$ is a particular cohomology class ${\omega }^{♮}\in {\mathrm{H}}^3(\mathbb{M},\mathrm{U}(1))$ that arises as a conformal field theoretic generalization of the second Chern class of a representation. This paper shows that ${\omega }^{♮}$ has order exactly $24$ and is not a Chern class. In order to perform this computation, this paper introduces a finite-group version of T-duality, which is used to relate ${\omega }^{♮}$ to the anomaly for the Leech lattice CFT.

23 pages. v3 contains substantial revisions to Section 2

References in corpus (2)

• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• A remark on ${\mathbb{Z}}_p$-orbifold constructions of the Moonshine vertex operator algebra

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• Third Homology of some Sporadic Finite Groups
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results
• Twisted Equivariant Tate K-Theory
• Bootstrapping Boundaries and Branes
• Topological Mathieu Moonshine