The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.
The Verlinde formula in logarithmic CFT
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abstract
In rational conformal field theory, the Verlinde formula computes the fusion coefficients from the modular S-transformations of the characters of the chiral algebra's representations. Generalising this formula to logarithmic models has proven rather difficult for a variety of reasons. Here, a recently proposed formalism (arXiv:1303.0847 [hep-th]) for the modular properties of certain classes of logarithmic theories is reviewed, and refined, using simple examples. A formalism addressing fusion rules in simple current extensions is also reviewed as a means to tackle logarithmic theories to which the proposed modular formalism does not directly apply.
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UNVERDICTED 2representative citing papers
Four-point functions in the bosonic ghost system have logarithmic singularities.
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Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules
The paper develops a formalism for reduction and inverse-reduction functors and computes the action of reduction on standard modules of V^k(sl_2), noting unbounded spectral sequences.
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Bosonic Ghost Correlators: A Case Study
Four-point functions in the bosonic ghost system have logarithmic singularities.