Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
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Publication:2283546
DOI10.1007/JHEP10(2019)268zbMATH Open1427.81136arXiv1906.08405WikidataQ126800307 ScholiaQ126800307MaRDI QIDQ2283546
Author name not available (Why is that?)
Publication date: 2 January 2020
Published in: (Search for Journal in Brave)
Abstract: Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic objects which compute higher-point global (scalar) conformal blocks in arbitrary spacetime dimensions, extending the result for the four-point block, known in the literature as a geodesic Witten diagram, to five- and six-point blocks. The main new tools which allow us to obtain such representations are various higher-point propagator identities, which can be interpreted as generalizations of the well-known flat space star-triangle identity, and which compute integrals over products of three bulk-to-bulk and/or bulk-to-boundary propagators in negatively curved spacetime. Using the holographic representation of the higher-point conformal blocks and higher-point propagator identities, we develop geodesic diagram techniques to obtain the explicit direct-channel conformal block decomposition of a broad class of higher-point AdS diagrams in a scalar effective bulk theory, with closed-form expressions for the decomposition coefficients. These methods require only certain elementary manipulations and no bulk integration, and furthermore provide quite trivially a simple algebraic origin of the logarithmic singularities of higher-point tree-level AdS diagrams. We also provide a more compact repackaging in terms of the spectral decomposition of the same diagrams, as well as an independent discussion on the closely related but computationally simpler framework over -adics which admits comparable statements for all previously mentioned results.
Full work available at URL: https://arxiv.org/abs/1906.08405
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