Autor(en)
Liu, Junyu; Perlmutter, Eric; Rosenhaus, Vladimir; Simmons-Duffin, David
Titel
d-dimensional SYK, AdS loops, and 6j symbols
Teil von
  • The journal of high energy physics, 2019-03, Vol.2019 (3), p.1-57
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Links zum Volltext
Quelle
DOAJ Directory of Open Access Journals
Beschreibungen
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 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 6j symbol, while one-loop n-gon diagrams are built out of 6j symbols.

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