Vertex operator expressions for Lie algebras of physical states

2024/08/14 by Thomas Driscoll-Spittler, Driscoll-Spittler, Thomas
Mathematics · #17B69 #Advanced Topics in Algebra #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2408.07597

openalex publication_date 2024/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Lie algebra of physical states associated with certain vertex operator algebras of central charge 24. By applying the no-ghost theorem from string theory we express the corresponding Lie brackets in terms of vertex algebra operations. In the special case of the Moonshine module this result answers a question of Borcherds, posed in his paper on the Monstrous moonshine conjecture.

Related

• Borcherds's Lie algebra and C₂-cofiniteness of vertex operator algebras of moonshine type
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