Closed-form expression for cross-channel conformal blocks near the lightcone

Abstract

In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalar primaries. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampé de Fériet function, which applies to intermediate operators of arbitrary spin in general dimensions. We derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our results for the lightcone limit also shed light on the complete analytic structure of conformal blocks in the lightcone expansion.

arXiv comment9 pages, 1 figure; v2: closed-form expression generalized to generic external scalars, references updated; v3: discussions improved, typos corrected, references updated; v4: published version

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• Higher-Point Conformal Blocks in the Comb Channel
• Helicity basis for three-dimensional conformal field theory
• Ising model close to $d=2$
• Efficient Rules for All Conformal Blocks
• Lightcone expansions of conformal blocks in closed form
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• More on Heavy-Light Bootstrap up to Double-Stress-Tensor
• Analytic Studies of Fermions in the Conformal Bootstrap