Logarithmic lift of the su(2)_{-1/2} model

Abstract

This paper carries on the investigation of the non-unitary su(2)_{-1/2} WZW model. An essential tool in our first work on this topic was a free-field representation, based on a c=-2 ηξghost system, and a Lorentzian boson. It turns out that there are several ``versions'' of the ηξsystem, allowing different su(2)_{-1/2} theories. This is explored here in details. In more technical terms, we consider extensions (in the c=-2 language) from the small to the large algebra representation and, in a further step, to the full symplectic fermion theory. In each case, the results are expressed in terms of su(2)_{-1/2} representations. At the first new layer (large algebra), continuous representations appear which are interpreted in terms of relaxed modules. At the second step (symplectic formulation), we recover a logarithmic theory with its characteristic signature, the occurrence of indecomposable representations. To determine whether any of these three versions of the su(2)_{-1/2} WZW is well-defined, one conventionally requires the construction of a modular invariant. This issue, however, is plagued with various difficulties, as we discuss.

28 pages, 9 figures, v2: presentation modified, version to be published

References in corpus (1)

• The su(2)_{-1/2} WZW model and the beta-gamma system

Cited by in corpus (33)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• Modular Data and Verlinde Formulae for Fractional Level WZW Models II
• The su(2)_{-1/2} WZW model and the beta-gamma system
• On the SU(2|1) WZW model and its statistical mechanics applications
• sl^(2)_{-1/2}: A Case Study
• Superconformal surfaces in four dimensions
• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• sl(2)_{-1/2} and the Triplet Model
• A modular invariant bulk theory for the c=0 triplet model
• Fusion algebra of critical percolation
• Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models
• The Verlinde formula in logarithmic CFT
• Superspace conformal field theory
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Modularity of logarithmic parafermion vertex algebras
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Affine Jordan cells, logarithmic correlators, and hamiltonian reduction
• Realizations of simple affine vertex algebras and their modules: the cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$
• Toward logarithmic extensions of ^sl(2)_k conformal field models
• Conformal superspace sigma-models
• The diagonal cosets of the Heisenberg group
• Coset construction of logarithmic minimal models: branching rules and branching functions
• Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
• Representations of the Nappi--Witten vertex operator algebra
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• Staggered modules of $N=2$ superconformal minimal models
• Staggered and affine Kac modules over $A_1^{(1)}$
• Bosonic Ghost Correlators: A Case Study