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.
$d$-dimensional SYK, AdS Loops, and $6j$ Symbols
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the $6j$ symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS. The contribution of the planar Feynman diagrams to the three-point function of the bilinear singlets in SYK is shown to be a $6j$ symbol. We generalize the computation of these and other Feynman diagrams to $d$ dimensions. The $6j$ symbol can be viewed as the crossing kernel for conformal partial waves, which may be computed using the Lorentzian inversion formula. We provide closed-form expressions for $6j$ symbols in $d=1,2,4$. In AdS, we show that the $6j$ symbol is the Lorentzian inversion of a crossing-symmetric tree-level exchange amplitude, thus efficiently packaging the double-trace OPE data. Finally, we consider one-loop diagrams in AdS with internal scalars and external spinning operators, and show that the triangle diagram is a $6j$ symbol, while one-loop $n$-gon diagrams are built out of $6j$ symbols.
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UNVERDICTED 5representative citing papers
Derives universal first-order ODEs governing the RG flow of boundary operator data (scaling dimensions, OPE and BOE coefficients) for 2D QFTs on hyperbolic space.
A neural-network approach with dispersion relations handles infinite OPE towers in thermal conformal correlators without positivity.
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
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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QFT as a set of ODEs
Derives universal first-order ODEs governing the RG flow of boundary operator data (scaling dimensions, OPE and BOE coefficients) for 2D QFTs on hyperbolic space.
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Neural Networks, Dispersion Relations and the Thermal Bootstrap
A neural-network approach with dispersion relations handles infinite OPE towers in thermal conformal correlators without positivity.
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Strongly Coupled Quantum Field Theory in Anti-de Sitter Spacetime
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.
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Notes on Tensor Models and Tensor Field Theories
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.