Construction and classification of holomorphic vertex operator algebras
TLDR
In this article, an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras was developed, and it was shown that Schellekens' classification of $V_1$-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operators.Abstract:
We develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens' classification of $V_1$-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.read more
Citations
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Monstrous BPS-algebras and the superstring origin of moonshine
TL;DR: In this article, the McKay-Thompson series T-g, g epsilon M can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models.
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Parafermion vertex operator algebras and -algebras
Journal ArticleDOI
Logarithmic conformal field theory, log-modular tensor categories and modular forms
Thomas Creutzig,Terry Gannon +1 more
TL;DR: In this article, the authors consider the more general class of logarithmic conformal field theories and vertex operator algebras and suggest that their modular pillar are trace functions with insertions corresponding to intertwiners of the projective cover of the vacuum, and the categorical pillar are finite tensor categories.
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A mathematical theory of gapless edges of 2d topological orders. Part I
Liang Kong,Hao Zheng,Hao Zheng +2 more
TL;DR: In this article, a unified mathematical theory of gapped and gapless edges of 2D topological orders was proposed, which includes the notion of a unitary fusion category as a special case of a gapped edge.
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Reconstruction and local extensions for twisted group doubles, and permutation orbifolds
David Evans,Terry Gannon +1 more
TL;DR: In this article, the first nontrivial reconstruction theorem for modular tensor categories was proved for permutation orbifolds of holomorphic conformal nets, and the branching coefficients of all possible local (conformal) extensions of any finite group orbifold of a holomorphic CONNAL net were derived.
References
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Book
Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Journal Article
Vertex operator algebras and the Monster
TL;DR: In this paper, complex realizations of vertex operator algebraic expressions are presented, and the main theorem of complex realisation of vertices operator algebra is proved. But the complexity is not discussed.
Journal ArticleDOI
Vertex algebras, Kac-Moody algebras, and the Monster.
TL;DR: An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.
Book
Vertex algebras for beginners
TL;DR: In this paper, a formal distribution a(z,w) = 2 QFT and chiral algebras is defined and the Virasoro algebra is defined, which is a generalization of the Wightman axioms.
Book
On Axiomatic Approaches to Vertex Operator Algebras and Modules
TL;DR: In this paper, the vertex operator algebras duality for vertex operators and vertex operators for modules is discussed, as well as the duality of vertex operators on modules.