The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS diagrams.
On the Polyakov-Mellin bootstrap
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We elaborate on some general aspects of the crossing symmetric approach of Polyakov to the conformal bootstrap, as recently formulated in Mellin space. This approach uses, as building blocks, Witten diagrams in AdS. We show the necessity for having contact Witten diagrams, in addition to the exchange ones, in two different contexts: a) the large $c$ expansion of the holographic bootstrap b) in the $\epsilon$ expansion at subleading orders to the ones studied already. In doing so, we use alternate simplified representations of the Witten diagrams in Mellin space. This enables us to also obtain compact, explicit expressions (in terms of a ${}_7F_6$ hypergeometric function!) for the analogue of the crossing kernel for Witten diagrams i.e., the decomposition into $s$-channel partial waves of crossed channel exchange diagrams.
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Introduces a cut-diagrammatic framework to apply crossing symmetry to individual topologies in large-N CFT correlators and computes associated OPE data for higher-trace operators.
Derives explicit OPE coefficients for contact and exchange Witten diagrams and closed-form defect-to-bulk crossing kernels for zero- and surface defects in specific dimensions.
citing papers explorer
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Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS diagrams.
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Higher-Trace Operators and Cut Diagrammatics in the Conformal Block Expansion
Introduces a cut-diagrammatic framework to apply crossing symmetry to individual topologies in large-N CFT correlators and computes associated OPE data for higher-trace operators.
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Aspects of Witten Diagrams for Holographic Defects
Derives explicit OPE coefficients for contact and exchange Witten diagrams and closed-form defect-to-bulk crossing kernels for zero- and surface defects in specific dimensions.