Affine vertex operator algebras and modular linear differential equations

DOI10.1007/s11005-016-0837-7zbMath1338.81344OpenAlexW2336935869MaRDI QIDQ282958

Kiyokazu Nagatomo, Yuichi Sakai, Yusuke Arike, Masanobu Kaneko

Publication date: 13 May 2016

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2324/4753038

zbMATH Keywords

modular invariance2-dimensional conformal field theoryaffine vertex operator algebramodular linear differential equation

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40)

Related Items (17)

The third order modular linear differential equations ⋮ Modular linear differential equations of fourth order and minimal \(\mathcal{W}\)-algebras ⋮ Towards a classification of two-character rational conformal field theories ⋮ Meromorphic cosets and the classification of three-character CFT ⋮ Modularity of Nahm sums for the tadpole diagram ⋮ Classification of some vertex operator algebras of rank 3 ⋮ Vertex operator algebras, minimal models, and modular linear differential equations of order 4 ⋮ Quasimodular forms as solutions of modular differential equations ⋮ Characterization of the simple Virasoro vertex operator algebras with 2 and 3-dimensional space of characters ⋮ Wronskian indices and rational conformal field theories ⋮ Hecke relations in rational conformal field theory ⋮ Vertex operator algebras with central charge 8 and 16 ⋮ Five not-so-easy pieces: open problems about vertex rings ⋮ Vertex operator algebras and modular invariance ⋮ Modular ordinary differential equations on \(\mathrm{SL}(2,\mathbb{Z})\) of third order and applications ⋮ Rational CFT with three characters: the quasi-character approach ⋮ Classifying three-character RCFTs with Wronskian index equalling 0 or 2

Cites Work

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• Infinite-dimensional Lie algebras, theta functions and modular forms
• Modular and conformal invariance constraints in representation theory of affine algebras
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• Ramanujan's ``lost notebook and the Virasoro algebra
• Virasoro algebra, Dedekind \(\eta\)-function, and specialized Macdonald identities
• From Dynkin diagram symmetries to fixed point structures
• Modular forms and second order ordinary differential equations: applications to vertex operator algebras
• Modular invariance of characters of vertex operator algebras
• VECTOR-VALUED MODULAR FORMS AND LINEAR DIFFERENTIAL OPERATORS
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.
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