dorsal/arxiv
View SchemaGenus-zero modular functors and intertwining operator algebras
| Authors | Yi-Zhi Huang |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712039 |
| URL | https://arxiv.org/abs/q-alg/9712039 |
Abstract
In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing intertwining operator algebras from representations of suitable vertex operator algebras were solved implicitly earlier in [H3] (q-alg/9505019). In the present paper, we generalize the geometric and operadic formulation of the notion of vertex operator algebra given in [H1], [H2], [HL1] (hep-th/9301009), [HL2] and [H6] to the notion of intertwining operator algebra. We show that the category of intertwining operator algebras of central charge c is isomorphic to the category of algebras over rational genus-zero modular functors (certain analytic partial operads) of central charge c satisfying certain generalized meromorphicity. This result is one main step in the construction of genus-zero conformal field theories from representations of vertex operator algebras announced in [H5] (q-alg/9512024). One byproduct of the proof of the present isomorphism theorem is a geometric construction of (framed) braid group representations from intertwining operator algebras and thus from representations of suitable vertex operator algebras.
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"abstract": "In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the\nnotion of intertwining operator algebra, a nonmeromorphic generalization of the\nnotion of vertex operator algebra involving monodromies. The problem of\nconstructing intertwining operator algebras from representations of suitable\nvertex operator algebras were solved implicitly earlier in [H3]\n(q-alg/9505019). In the present paper, we generalize the geometric and operadic\nformulation of the notion of vertex operator algebra given in [H1], [H2], [HL1]\n(hep-th/9301009), [HL2] and [H6] to the notion of intertwining operator\nalgebra. We show that the category of intertwining operator algebras of central\ncharge c is isomorphic to the category of algebras over rational genus-zero\nmodular functors (certain analytic partial operads) of central charge c\nsatisfying certain generalized meromorphicity. This result is one main step in\nthe construction of genus-zero conformal field theories from representations of\nvertex operator algebras announced in [H5] (q-alg/9512024). One byproduct of\nthe proof of the present isomorphism theorem is a geometric construction of\n(framed) braid group representations from intertwining operator algebras and\nthus from representations of suitable vertex operator algebras.",
"arxiv_id": "q-alg/9712039",
"authors": [
"Yi-Zhi Huang"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "Genus-zero modular functors and intertwining operator algebras",
"url": "https://arxiv.org/abs/q-alg/9712039"
},
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