Algebraic orbifold conformal field theories

Abstract

We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a unitary modular category. Many new unitary modular categories are obtained. We also show that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time.

24 pages, Amstex

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Cited by in corpus (27)

• Local conformal nets arising from framed vertex operator algebras
• Solitons in Affine and Permutation Orbifolds
• Conformal Orbifold Theories and Braided Crossed G-Categories
• Conformal Field Theory, Tensor Categories and Operator Algebras
• The Moonshine Anomaly
• Generalized Orbifold Construction for Conformal Nets
• Representations of Conformal Nets, Universal C*-Algebras and K-Theory
• Spontaneous symmetry breaking from anyon condensation
• Subfactors and Mathematical Physics
• Models in Boundary Quantum Field Theory Associated with Lattices and Loop Group Models
• Some computations in the cyclic permutations of completely rational nets
• Categorification of algebraic quantum field theories
• Higher Coxeter graphs associated to affine su(3) modular invariants
• Infinite index extensions of local nets and defects
• Quantum Operations on Conformal Nets
• Conformal Net Realizability of Tambara-Yamagami Categories and Generalized Metaplectic Modular Categories
• Examples of subfactors from conformal field theory
• Braided categories of endomorphisms as invariants for local quantum field theories
• Intersections of finite families of finite index subfactors
• Representations of the orbifold VOAS $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^K$ and the commutant VOAS $C_{{L_{\widehat{{\mathfrak{so}}_m}}(1,0)}^{\otimes 3}}(L_{\widehat{{\mathfrak{so}}_m}}(3,0))$
• Orbifolds and minimal modular extensions
• From Operator Algebras to Superconformal Field Theory
• On Induction for Twisted Representations of Conformal Nets
• Vertex operator superalgebras and 16-fold way
• Representations and fusion rules for the orbifold vertex operator algebras $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$
• S-matrix in orbifold theory
• Topological Quantum Field Theories and Operator Algebras