From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory

DOI10.1073/pnas.0501135102zbMath1112.17030arXivmath/0504311OpenAlexW2145631582WikidataQ33936705 ScholiaQ33936705MaRDI QIDQ5293359

James Lepowsky

Publication date: 30 June 2007

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504311

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) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Categorical structures (18D99)

Related Items (4)

VERTEX OPERATOR ALGEBRAS AND THE VERLINDE CONJECTURE ⋮ RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES ⋮ Cofiniteness conditions, projective covers and the logarithmic tensor product theory ⋮ Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules

Cites Work

• Fusion rules and modular transformations in 2D conformal field theory
• Infinite conformal symmetry in two-dimensional quantum field theory
• A theory of tensor products for module categories for a vertex operator algebra. IV
• Virasoro vertex operator algebras, the (nonmeromomorphic) operator product expansion and the tensor product theory
• Vertex algebras, Kac-Moody algebras, and the Monster
• Modular invariance of characters of vertex operator algebras
• Vertex operator algebras, the Verlinde conjecture, and modular tensor categories
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.

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