TY - JOUR

T1 - Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, I

AU - Huang, Yi Zhi

AU - Milas, Antun

N1 - Funding Information:
The research of Y.-Z. Huang is supported in part by NSF grant DMS-9622961. The research of A. Milas is supported in part by NSF grants.

PY - 2002

Y1 - 2002

N2 - We apply the general theory of tensor products of modules for a vertex operator algebra (developed by Lepowsky and the first author) and the general theory of intertwining operator algebras (developed by the first author) to the case of the N = 1 superconformal minimal models and related models in superconformal field theory. We show that for the category of modules for a vertex operator algebra containing a subalgebra isomorphic to a tensor product of rational vertex operator superalgebras associated to the N = 1 Neveu-Schwarz Lie superalgebra, the intertwining operators among the modules have the associativity property, the category has a natural structure of vertex tensor category, and a number of related results hold. We obtain, as a corollary and special case, a construction of a braided tensor category structure on the category of finite direct sums of minimal modules of central charge cp,q = 3/2(1 - 2 (p-q)2/pq) for the N = 1 Neveu-Schwarz Lie superalgebra for any fixed integers p, q larger than 1 such that p - q ∈ 2ℤ and (p - q)/2 and q relatively prime to each other.

AB - We apply the general theory of tensor products of modules for a vertex operator algebra (developed by Lepowsky and the first author) and the general theory of intertwining operator algebras (developed by the first author) to the case of the N = 1 superconformal minimal models and related models in superconformal field theory. We show that for the category of modules for a vertex operator algebra containing a subalgebra isomorphic to a tensor product of rational vertex operator superalgebras associated to the N = 1 Neveu-Schwarz Lie superalgebra, the intertwining operators among the modules have the associativity property, the category has a natural structure of vertex tensor category, and a number of related results hold. We obtain, as a corollary and special case, a construction of a braided tensor category structure on the category of finite direct sums of minimal modules of central charge cp,q = 3/2(1 - 2 (p-q)2/pq) for the N = 1 Neveu-Schwarz Lie superalgebra for any fixed integers p, q larger than 1 such that p - q ∈ 2ℤ and (p - q)/2 and q relatively prime to each other.

KW - Intertwining operator superalgebras

KW - Superconformal algebras

KW - Vertex tensor categories

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U2 - 10.1142/S0219199702000622

DO - 10.1142/S0219199702000622

M3 - Article

AN - SCOPUS:0036015420

SN - 0219-1997

VL - 4

SP - 327

EP - 355

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 2

ER -