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

Robert Coquereaux (1, 2) , Gil Schieber (1, 3, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 CBPF - Centro Brasileiro de Pesquisas Físicas

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)).

Mots clés: conformal field theories; quantum groupoids; quantum symmetries; modular invariance; conformal field theories.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Algèbres quantiques [math.QA]

Robert Coquereaux, Gil Schieber. From conformal embeddings to quantum symmetries: an exceptional SU(4) example. 2007. ⟨hal-00177273v2⟩