2019/06/30 by Heng-Yu Chen, Hideki Kyono
Mathematics · Physics and Astronomy · #Analytic continuation #Black Holes and Theoretical Physics #Conformal map #Geometric Analysis and Curvature Flows #Hypergeometric function #Hypergeometric identity #Minkowski space #Noncommutative and Quantum Gravity Theories #Operator (biology) #Singularity #Spacetime #TRACE (psycholinguistics) #hep-th
paper · pdf · doi:10.1007/jhep10(2019)149
37 pages, 7 figures. Various references added and typos corrected
openalex created_date 2019/06/14 · arxiv created 2019/07/31 · openalex publication_date 2019/10/01 · arxiv updated 2020/01/08 · openalex updated_date 2026/08/05
A bstract 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 F 4. 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.