A multipoint conformal block chain in d dimensions

• Published in: The journal of high energy physics Vol. 2020; no. 5; pp. 1 - 50
• Main Author: Parikh, Sarthak
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; Conformal and W Symmetry; Conformal Field Theory; Cryptography; Elementary Particles; High energy physics; Holography; Hypergeometric functions; Identities; Operators (mathematics); Physics; Physics and Astronomy; Power series; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Series expansion; String Theory; Thermal expansion; AdS-CFT Correspondence; Conformal Field Theory; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2020)120

A bstract Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we systematically work out the d -dimensional n -point global conformal blocks (for arbitrary d and n ) for external and exchanged scalar operators in the so-called comb channel. We use kinematic aspects of holography and previously worked out higher-point AdS propagator identities to first obtain the geodesic diagram representation for the ( n + 2)-point block. Subsequently, upon taking a particular double-OPE limit, we obtain an explicit power series expansion for the n -point block expressed in terms of powers of conformal cross-ratios. Interestingly, the expansion coefficient is written entirely in terms of Pochhammer symbols and ( n − 4) factors of the generalized hypergeometric function 3 F 2 , for which we provide a holographic explanation. This generalizes the results previously obtained in the literature for n = 4 , 5. We verify the results explicitly in embedding space using conformal Casimir equations.