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Journal of High Energy Physics

, 2019:149 | Cite as

On conformal blocks, crossing kernels and multi-variable hypergeometric functions

  • Heng-Yu Chen
  • Hideki KyonoEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function F4. We also construct its generalization to the non-local primary exchange operator with continuous spin and its corresponding Mellin representation which are relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute the so-called crossing kernel in general spacetime dimensions, the resultant expression can be written as a double infinite summation over certain Kampé de Fériet hypergeometric functions with the correct double trace operator singularity structures. We also include some complementary computations in AdS space, demonstrating the orthogonality of conformal blocks and performing the decompositions.

Keywords

AdS-CFT Correspondence Conformal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsNational Taiwan UniversityTaipeiTaiwan
  2. 2.Department of PhysicsKyoto UniversityKyotoJapan

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