Universal RCFT Correlators from the Holomorphic Bootstrap

Abstract

We elaborate and extend the method of Wronskian differential equations for conformal blocks to compute four-point correlation functions on the plane for classes of primary fields in rational (and possibly more general) conformal field theories. This approach leads to universal differential equations for families of CFT's and provides a very simple re-derivation of the BPZ results for the degenerate fields ${\varphi }_{1,2}$ and ${\varphi }_{2,1}$ in the c < 1 minimal models. We apply this technique to compute correlators for the WZW models corresponding to the Deligne-Cvitanović exceptional series of Lie algebras. The application turns out to be subtle in certain cases where there are multiple decoupled primaries. The power of this approach is demonstrated by applying it to compute four-point functions for the Baby Monster CFT, which does not belong to any minimal series.

37 pages. This version corrects some errors/typos and supersedes the published version, though the main conclusions remain unaffected. Some formulae for conformal blocks have been completed/corrected relative to the previous version, and the formula for combining blocks into correlators has also been corrected

References in corpus (4)

• Logarithmic torus amplitudes
• Current Algebra on the Torus
• Two-dimensional RCFT's without Kac-Moody symmetry
• Modular differential equations for torus one-point functions

Cited by in corpus (10)

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• Towards a Classification of Two-Character Rational Conformal Field Theories
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• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Wronskian Indices and Rational Conformal Field Theories
• Curiosities above c = 24
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Universal Correlators and Novel Cosets in 2d RCFT