A multipoint conformal block chain in \(d\) dimensions
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Publication:779391
DOI10.1007/JHEP05(2020)120zbMATH Open1437.83116arXiv1911.09190MaRDI QIDQ779391
Author name not available (Why is that?)
Publication date: 21 July 2020
Published in: (Search for Journal in Brave)
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 -dimensional -point global conformal blocks (for arbitrary and ) 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 -point block. Subsequently, upon taking a particular double-OPE limit, we obtain an explicit power series expansion for the -point block expressed in terms of powers of conformal cross-ratios. Interestingly, the expansion coefficient is written entirely in terms of Pochhammer symbols and factors of the generalized hypergeometric function , for which we provide a holographic explanation. This generalizes the results previously obtained in the literature for . We verify the results explicitly in embedding space using conformal Casimir equations.
Full work available at URL: https://arxiv.org/abs/1911.09190
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