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The journal of high energy physics, 2019-03, Vol.2019 (3), p.1-57, Article 52
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2019
Quelle
Free E-Journal (出版社公開部分のみ)
Beschreibungen/Notizen
A
bstract
We study the 6
j
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 6
j
symbol. We generalize the computation of these and other Feynman diagrams to
d
dimensions. The 6
j
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 6
j
symbols in
d
= 1, 2, 4. In AdS, we show that the 6
j
symbol is the Lorentzian inversion of a crossing-symmetric tree-level exchange amplitude, thus efficiently packaging the doubletrace 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 6
j
symbol, while one-loop
n
-gon diagrams are built out of 6
j
symbols.