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A unitary tensor product theory for unitary vertex operator algebra modules

dc.creatorGui, Bin
dc.description.abstractLet V be a unitary vertex operator algebra (VOA) satisfying the following conditions: (1) V is of CFT type. (2) Every N-gradable weak V -module is completely reducible. (3) V is C2-cofinite. Let Rep(V)be the category of unitary V -modules, and let C be a subcategory of Rep(V) whose objects are closed under taking tensor product. Then C is a ribbon fusion category. For any objects Wi; Wj of C, we define a sesquilinear form on the tensor product Wi bWj. We show that if these sesquilinear forms are positive definite (i.e., when they are inner products), then the ribbon category C is unitary. We show that if the unitary V -modules and a generating set of intertwining operators in C satisfy certain energy bounds, then these sesquilinear forms are positive definite. Our result can be applied to the modular tensor categories associated to unitary Virasoro VOAs, and unitary affine VOAs of type An; Dn; G2, and more.
dc.subjectalgebraic quantum field theory
dc.subjecttensor category
dc.subjectconformal field theory
dc.subjectVertex operator algebra
dc.subjectunitary modular tensor category
dc.titleA unitary tensor product theory for unitary vertex operator algebra modules
dc.contributor.committeeMemberThomas Weiler
dc.contributor.committeeMemberJesse Peterson
dc.contributor.committeeMemberDietmar Bisch
dc.contributor.committeeMemberAkram Aldroubi
dc.type.materialtext University
dc.contributor.committeeChairVaughan Jones

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