Year: 2020
Type: article
Abstract: 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.
Source: Journal of High Energy Physics
Author: Sarthak Parikh
Institution: California Institute of Technology
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2991094650