Modularity in Orbifold Theory for Vertex Operator Superalgebras

2004/11/23 by Chongying Dong, Zhongping Zhao · 40 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Automorphism #Holomorphic function #Operator (biology) #Operator algebra #Orbifold #Representation theory #Superalgebra #Vertex (graph theory) #math.QA #math.RT #msc:17B69

paper · pdf · doi:10.1007/s00220-005-1418-2

published in Communications in Mathematical Physics 260(1), 227-256 (Springer Science+Business Media) · 31 pages

arxiv created 2004/11/23 · openalex publication_date 2005/08/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

This paper is about the orbifold theory for vertex operator superalgebras. Given a vertex operator superalgebra V and a finite automorphism group G of V, we show that the trace functions associated to the twisted sectors are holomorphic in the upper half plane for any commuting pairs in G under the C₂-cofinite condition. We also establish that these functions afford a representation of the full modular group if V is C₂-cofinite and g-rational for any g in G.

Citations

• Monstrous moonshine and monstrous Lie superalgebras
• Local systems of vertex operators, vertex superalgebras and modules
• The friendly giant
• Vertex algebras, Kac-Moody algebras, and the Monster
• Meromorphicc=24 conformal field theories
• Classical and quantum conformal field theory
• Monstrous Moonshine