On orbifold theory

DOI10.1016/j.aim.2017.09.032zbMath1419.17031arXiv1507.03306OpenAlexW2963540294MaRDI QIDQ1673979

Peng Zhang

Publication date: 30 October 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.03306

zbMATH Keywords

vertex operator algebraorbifold theory

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Vertex operators; vertex operator algebras and related structures (17B69) Topology and geometry of orbifolds (57R18)

Related Items (48)

The \(\mathbb{Z}_2\)-orbifold of the \(\mathcal{W}_3\)-algebra ⋮ Permutation orbifolds of Virasoro vertex algebras and \(W\)-algebras ⋮ Sigma involutions associated with parafermion vertex operator algebra K(sl2,k) ⋮ Character rings and fusion algebras ⋮ Much ado about Mathieu ⋮ Trace functions of the parafermion vertex operator algebras ⋮ \(G\)-twisted associative algebras of vertex operator superalgebras ⋮ \(S\)-matrix in permutation orbifolds ⋮ Super orbifold theory ⋮ Twisted representations for S-local vertex operator algebras ⋮ Natural construction of ten Borcherds-Kac-Moody algebras associated with elements in \(M_{23}\) ⋮ Representations of \(\mathbb{Z}_2\)-orbifold of the parafermion vertex operator algebra \(K(sl_{2},k)\) ⋮ Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras ⋮ Orbifolds of lattice vertex algebras ⋮ Congruence property in orbifold theory ⋮ Geometric positivity of the fusion products of unitary vertex operator algebra modules ⋮ Orbifold theory for vertex algebras and Galois correspondence ⋮ \(S_3\)-permutation orbifolds of Virasoro vertex algebras ⋮ Associative algebras of \(\mathbb{Z}\)-graded vertex operator superalgebras and their applications ⋮ Lattices, vertex algebras, and modular categories ⋮ Inertia groups and uniqueness of holomorphic vertex operator algebras ⋮ \(S\)-matrix in orbifold theory ⋮ Unnamed Item ⋮ Fusion rules for \(\mathbb{Z}_2\)-orbifolds of affine and parafermion vertex operator algebras ⋮ On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras ⋮ Representations of the orbifold VOAS \(L_{\widehat{\mathfrak{sl}_2}}(k,0)^K\) and the commutant VOAS \(C_{{L_{\widehat{\mathfrak{so}_m}}(1,0)}^{\otimes 3}}({L_{\widehat{\mathfrak{so}_m}}(3,0)})\) ⋮ Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory ⋮ On \(\mathbb {Z}_p\)-orbifold constructions of the Moonshine vertex operator algebra ⋮ Representations and fusion rules for the orbifold vertex operator algebras Lsl2̂(k,0)Zp ⋮ The irreducible modules and fusion rules for the parafermion vertex operator algebras ⋮ Cyclic orbifolds of lattice vertex operator algebras having group-like fusions ⋮ Vertex operator superalgebras and the 16-fold way ⋮ 2-permutations of lattice vertex operator algebras: higher rank ⋮ The 3-permutation orbifold of a lattice vertex operator algebra ⋮ Generators, spanning sets and existence of twisted modules for a grading-restricted vertex (super)algebra ⋮ Hopf actions on vertex operator algebras ⋮ Extensions of tensor products of \(\mathbb{Z}_p\)-orbifold models of the lattice vertex operator algebra \(V_{\sqrt{2} A_{p - 1}}\) ⋮ Non-abelian orbifolds of lattice vertex operator algebras ⋮ Construction and classification of holomorphic vertex operator algebras ⋮ The large \(N\) limit of orbifold vertex operator algebras ⋮ Simple Whittaker modules over free bosonic orbifold vertex operator algebras ⋮ The \(\mathbb{Z}_2\)-orbifold of the universal affine vertex algebra ⋮ Permutation orbifolds of 𝔰𝔩2 vertex operator algebras ⋮ Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras ⋮ Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras ⋮ Unnamed Item ⋮ Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra ⋮ Reconstruction and local extensions for twisted group doubles, and permutation orbifolds

Cites Work

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• On quantum Galois theory
• Fusion rules and modular transformations in 2D conformal field theory
• Congruence property in conformal field theory
• Vertex operator algebras and associative algebras
• Some finiteness properties of regular vertex operator algebras
• Generalized vertex algebras and relative vertex operators
• Vertex algebras associated with even lattices
• Twisted modules for vertex algebras associated with even lattices
• Regularity of rational vertex operator algebras
• Twisted representations of vertex operator algebras
• Uniform product of \(A_{g,n}(V)\) for an orbifold model \(V\) and \(G\)-twisted Zhu algebra.
• Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms
• \(\mathbb{Z}\)-graded weak modules and regularity
• Solitons in affine and permutation orbifolds
• On intertwining operators and finite automorphism groups of vertex operator algebras
• Modular categories and orbifold models
• Twisted sectors for tensor product vertex operator algebras associated to permutation groups
• Vertex operator algebras, generalized doubles and dual pairs
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• A theory of tensor products for module categories for a vertex operator algebra. III
• A theory of tensor products for module categories for a vertex operator algebra. I
• A theory of tensor products for module categories for a vertex operator algebra. II
• The algebraic structure of relative twisted vertex operators
• Simple currents and extensions of vertex operator algebras
• Quantum Galois theory for finite groups
• \(C_2\)-cofiniteness of cyclic-orbifold models
• Braided tensor categories and extensions of vertex operator algebras
• On fusion categories.
• Quantum dimensions and quantum Galois theory
• VERTEX OPERATOR ALGEBRAS AND THE VERLINDE CONJECTURE
• Calculus of twisted vertex operators
• Remarks on Classical Invariant Theory
• Algebraic orbifold conformal field theories
• The irreducible modules and fusion rules for the parafermion vertex operator algebras
• Rationality, regularity, and 𝐶₂-cofiniteness
• Modular invariance of characters of vertex operator algebras
• The Witt group of non-degenerate braided fusion categories
• On axiomatic approaches to vertex operator algebras and modules
• Twisted group algebras and their representations
• Quasi Hopf algebras, group cohomology and orbifold models
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.

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