TFT construction of RCFT correlators IV: Structure constants and correlation functions

Abstract

We compute the fundamental correlation functions in two-dimensional rational conformal field theory, from which all other correlators can be obtained by sewing: the correlators of three bulk fields on the sphere, one bulk and one boundary field on the disk, three boundary fields on the disk, and one bulk field on the cross cap. We also consider conformal defects and calculate the correlators of three defect fields on the sphere and of one defect field on the cross cap. Each of these correlators is presented as the product of a structure constant and the appropriate conformal two- or three-point block. The structure constants are expressed as invariants of ribbon graphs in three-manifolds.

98 pages, some figures; v2 (version published in NPB): typos corrected

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• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
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• Hamiltonian anomalies from extended field theories
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• Type $II$ quantum subgroups of ${\mathfrak{sl}}_N$. $I$: Symmetries of local modules
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models