Preprint 106/2005

Full field algebras

Yi-Zhi Huang and Liang Kong

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Submission date: 18. Nov. 2005
Pages: 68
published in: Communications in mathematical physics, 272 (2007) 2, p. 345-396 
DOI number (of the published article): 10.1007/s00220-007-0224-4
MSC-Numbers: 17B69, 81T40
Keywords and phrases: full field algebra, conformal field theory
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We introduce a notion of full field algebra which is essentially an algebraic formulation of the notion of genus-zero full conformal field theory. For any vertex operator algebras formula13 and formula15, formula17 is naturally a full field algebra and we introduce a notion of full field algebra over formula17. We study the structure of full field algebras over formula17 using modules and intertwining operators for formula13 and formula15. For a simple vertex operator algebra V satisfying certain natural finitely reductive conditions needed for the Verlinde conjecture to hold, we construct a bilinear form on the space of intertwining operators for V and prove the nondegeneracy and other basic properties of this form. The proof of the nondegenracy of the bilinear form depends not only on the theory of intertwining operator algebras but also on the modular invariance for intertwining operator algebras through the use of the results obtained in the proof of the Verlinde conjecture by the first author. Using this nondegenerate bilinear form, we construct a full field algebra over formula31 and an invariant bilinear form on this algebra.

20.02.2013, 14:49