Multipoint Conformal Blocks in the Comb Channel

Abstract

Conformal blocks are the building blocks for correlation functions in conformal field theories. The four-point function is the most well-studied case. We consider conformal blocks for $n$-point correlation functions. For conformal field theories in dimensions $d=1$ and $d=2$, we use the shadow formalism to compute $n$-point conformal blocks, for arbitrary $n$, in a particular channel which we refer to as the comb channel. The result is expressed in terms of a multivariable hypergeometric function, for which we give series, differential, and integral representations. In general dimension $d$ we derive the $5$-point conformal block, for external and exchanged scalar operators.

arXiv comment39 pages

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• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
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• Spinors and conformal correlators
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• How to Succeed at Witten Diagram Recursions without Really Trying
• Analytic Studies of Fermions in the Conformal Bootstrap
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