Modular data and Verlinde formulae for fractional level WZW models I

DOI10.1016/j.nuclphysb.2012.07.018zbMath1262.81157arXiv1205.6513OpenAlexW2166597665MaRDI QIDQ1950083

Thomas Creutzig, David Ridout

Publication date: 8 May 2013

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.6513

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items (49)

Weight representations of admissible affine vertex algebras ⋮ An admissible level \(\widehat{\mathfrak{osp}}(1| 2)\)-model: modular transformations and the Verlinde formula ⋮ Modularity of logarithmic parafermion vertex algebras ⋮ Fusion rules for the logarithmicN= 1 superconformal minimal models: I. The Neveu–Schwarz sector ⋮ Negative index Jacobi forms and quantum modular forms ⋮ Braided tensor categories of admissible modules for affine Lie algebras ⋮ Modularity of Bershadsky-Polyakov minimal models ⋮ Relaxed highest-weight modules. I: Rank 1 cases ⋮ W-algebras for Argyres-Douglas theories ⋮ Characters of Modules of Irrational Vertex Algebras ⋮ A Kazhdan-Lusztig correspondence for \(L_{-\frac{3}{2}}(\mathfrak{sl}_3)\) ⋮ Logarithmic conformal field theory, log-modular tensor categories and modular forms ⋮ Coset constructions of logarithmic \((1, p)\) models ⋮ Higgs and Coulomb branches from vertex operator algebras ⋮ Rigid tensor structure on big module categories for some \(W\)-(super)algebras in type \(A\) ⋮ The worldsheet dual of the symmetric product CFT ⋮ Admissible level \(\mathfrak{osp}(1|2)\) minimal models and their relaxed highest weight modules ⋮ Tensor Categories for Vertex Operator Superalgebra Extensions ⋮ Relaxed singular vectors, Jack symmetric functions and fractional level \(\widehat{\mathfrak{sl}}(2)\) models ⋮ Bimodule structure of the mixed tensor product over \(\mathcal{U}_q s \ell(2 | 1)\) and quantum walled Brauer algebra ⋮ JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS ⋮ Line defect Schur indices, Verlinde algebras and \(\mathrm{U}(1)_{r}\) fixed points ⋮ Modular data and Verlinde formulae for fractional level WZW models. II ⋮ Cosets, characters and fusion for admissible-level \(\mathfrak{osp}(1 | 2)\) minimal models ⋮ Logarithmic W-algebras and Argyres-Douglas theories at higher rank ⋮ Modular transformations and Verlinde formulae for logarithmic (\(p_+,p_-\))-models ⋮ Staggered modules of \(N = 2\) superconformal minimal models ⋮ Fusion categories for affine vertex algebras at admissible levels ⋮ Argyres-Douglas theories, chiral algebras and wild Hitchin characters ⋮ Representations of the Nappi-Witten vertex operator algebra ⋮ Logarithmic link invariants of \(\overline{U}_q^H(\mathfrak{sl}_2)\) and asymptotic dimensions of singlet vertex algebras ⋮ False theta functions and the Verlinde formula ⋮ Bosonic ghosts at \(c=2\) as a logarithmic CFT ⋮ The mock modular data of a family of superalgebras ⋮ Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras ⋮ Representation theory of $L_k(\mathfrak {osp}(1 \vert 2))$ from vertex tensor categories and Jacobi forms ⋮ From VOAs to short star products in SCFT ⋮ Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras ⋮ Boundary algebras and Kac modules for logarithmic minimal models ⋮ Simple current extensions beyond semi-simplicity ⋮ Schur-Weyl duality for Heisenberg cosets ⋮ Unitary and non-unitary \(N=2\) minimal models ⋮ Strings on $\mathrm{AdS}_3 \times S^3 \times S^3 \times S^1$ ⋮ Braided tensor categories related to \(\mathcal{B}_p\) vertex algebras ⋮ Superconformal surfaces in four dimensions ⋮ Admissible-level \(\mathfrak{sl}_3\) minimal models ⋮ Relaxed highest-weight modules II: Classifications for affine vertex algebras ⋮ Bosonic ghostbusting: the bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion ⋮ Fusion rules for the logarithmic \(N\)=1 superconformal minimal models. II: Including the Ramond sector

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