Genus-zero modular functors and intertwining operator algebras

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Abstract

In [7] and [9], the author introduced the notion of intertwining operator algebra, a non-meromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing intertwining operator algebras from representations of suitable vertex operator algebras was solved implicitly earlier in [5]. In the present paper, we generalize the geometric and operadic formulation of the notion of vertex operator algebra given in [3, 4, 11, 12, 8] to the notion of intertwining operator algebra. We show that the category of intertwining operator algebras of central charge c ∈ ℂ is isomorphic to the category of algebras over rational genus-zero modular functors (certain analytic partial operads) of central charge c satisfying a certain generalized meromorphicity property. This result is one main step in the construction of genus-zero conformal field theories from representations of vertex operator algebras announced in [7]. One byproduct of the proof of the present isomorphism theorem is a geometric construction of (framed) braid group representations from intertwining operator algebras and, in particular, from representations of suitable vertex operator algebras.

Original languageEnglish (US)
Pages (from-to)845-863
Number of pages19
JournalInternational Journal of Mathematics
Volume9
Issue number2
DOIs
StatePublished - Nov 1998

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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