Geometric interpretation of vertex operator algebras

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28 Scopus citations


In this paper, Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator construction of the Monster to give a geometric definition of vertex operator algebras. The main result announced is the equivalence between this definition and the algebraic one in the sense that the categories determined by these definitions are isomorphic.

Original languageEnglish (US)
Pages (from-to)9964-9968
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number22
StatePublished - 1991

All Science Journal Classification (ASJC) codes

  • General


  • Conformal field theory
  • Formal calculus
  • Virasoro algebra


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