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Title page for ETD etd-06272018-151541

Type of Document Dissertation
Author Gui, Bin
Author's Email Address binguimath@gmail.com
URN etd-06272018-151541
Title A unitary tensor product theory for unitary vertex operator algebra modules
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Vaughan Jones Committee Chair
Akram Aldroubi Committee Member
Dietmar Bisch Committee Member
Jesse Peterson Committee Member
Thomas Weiler Committee Member
  • algebraic quantum field theory
  • tensor category
  • conformal field theory
  • Vertex operator algebra
  • unitary modular tensor category
Date of Defense 2018-03-29
Availability unrestricted
Let 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.

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