Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries

Abstract

For every ADE Dynkin diagram, we give a realization, in terms of usual fusion algebras (graph algebras), of the algebra of quantum symmetries described by the associated Ocneanu graph. We give explicitly, in each case, the list of the corresponding twisted partition functions

47 pages, 25 figures and 17 tables. Several typos are corrected. References added

References in corpus (5)

• Generalised twisted partition functions
• The many faces of Ocneanu cells
• Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
• On q-analog of McKay correspondence and ADE classification of sl^(2) conformal field theories
• Classical and quantum polyhedra: A fusion graph algebra point of view

Cited by in corpus (26)

• TFT construction of RCFT correlators I: Partition functions
• Duality and defects in rational conformal field theory
• Kramers-Wannier duality from conformal defects
• Topological defects for the free boson CFT
• Reflection and Transmission for Conformal Defects
• TFT construction of RCFT correlators II: Unoriented world sheets
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Perturbed Defects and T-Systems in Conformal Field Theory
• Module categories, weak Hopf algebras and modular invariants
• Integrable and Conformal Twisted Boundary Conditions for sl(2) A-D-E Lattice Models
• From conformal embeddings to quantum symmetries: an exceptional SU(4) example
• Racah - Wigner quantum 6j Symbols, Ocneanu Cells for AN diagrams, and quantum groupoids
• Higher Coxeter graphs associated to affine su(3) modular invariants
• Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings
• Determination of quantum symmetries for higher ADE systems from the modular T matrix
• Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus
• Duality and conformal twisted boundaries in the Ising model
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• On quantum symmetries of the non--ADE graph F4
• The A2 Ocneanu quantum groupoid
• On the inner structure of a permutation: Bicolored Partitions and Eulerians, Trees and Primitives
• Torus structure on graphs and twisted partition functions for minimal and affine models
• Lattice Realizations of the Open Descendants of Twisted Boundary Conditions for sl(2) A-D-E Models
• Paths on graphs and associated quantum groupoids
• Quantum symmetries of faces models and the double triangle algebra