From conformal embeddings to quantum symmetries: an exceptional SU(4) example

Abstract : We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a quantum graph. For known examples, the corresponding modular invariant partition function, which is sometimes associated with a conformal embedding, provides enough information to recover the whole structure. We illustrate these notions with the example of the conformal embedding of SU(4) at level 4 into Spin(15) at level 1, leading to the exceptional quantum graph E4(SU(4)).
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  • HAL Id : hal-00177273, version 3
  • ARXIV : 0710.1397

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Robert Coquereaux, Gil Schieber. From conformal embeddings to quantum symmetries: an exceptional SU(4) example. Journal of Physics: Conference Series, IOP Publishing, 2008, 103, pp.012006. ⟨hal-00177273v3⟩

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