Logarithmic Parafermion Vertex Operator Algebras

• Author / Creator

  Auger, Jean

• This thesis is about the theory of vertex operator algebras and their representations. Its main results provide new examples of logarithmic C2-cofinite vertex operator algebras. These include closure of the characters under modular transformations with explicit determination of the modular coefficients for an infinite family of parafermionic vertex operator algebras and proofs of C2-cofiniteness for a few specific levels including for three new cases. The rest of the work presented in this thesis provides a new comprehension of the notoriously difficult proof of the Kac-Wakimoto character formula, but also categorical results and tools to study certain vertex operator algebras' categories involving infinite direct sums.

• Subjects / Keywords

  • relaxed highest weight
  • direct sum completion
  • Kac-Wakimoto
  • vvmf
  • conformal field theory
  • ind category
  • VOA
  • affine
  • ind object
  • vertex
  • tensor categories
  • simple current extension
  • parafermion
  • modular form
  • C2-cofiniteness
  • c2-cofiniteness
  • voa
  • braided
  • infinite extension
  • monoidal categories
  • modularity
  • VVMF
  • vertex operator
  • representation theory

• Graduation date

  Fall 2018

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3FF3MG26

• License

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