Vertex algebras, topological defects, and Moonshine

2024/12/30 by Roberto Volpato, Volpato, Roberto · 1 citation
Computer Science · #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2412.21141

Abstract

We discuss topological defect lines in holomorphic vertex operators algebras and superalgebras, in particular Frenkel-Lepowsky-Meurman Monster VOA V^\natural with central charge c=24, and Conway module SVOA V^f\natural with c=12. First, we consider duality defects in V^\natural for all non-anomalous Fricke elements of the Monster group, and provide a general formula for the corresponding defect McKay-Thompson series. Furthermore, we describe some general properties of the category of defect lines preserving the N=1 superVirasoro algebra in V^f\natural. We argue that, under some mild assumptions, every such defect in V^f\natural is associated with a ℤ-linear map form the Leech lattice to itself. This correspondence establishes a surjective (not injective) ring homomorphism between the Grothendieck ring of the category of topological defects and the ring of Leech lattice endomorphisms. Finally, we speculate about possible generalization of the Moonshine conjectures that include topological defect lines.

Cited by

• Towards a classification of topological defects in K3 sigma models

Related

• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results
• On the uniqueness of the moonshine vertex operator algebra
• A new construction of the moonshine vertex operator algebra over the real number field
• Vertex operator algebras, extended E₈ diagram, and McKay's observation on the Monster simple group
• The Moonshine Module for Conway's Group