Details

Autor(en) / Beteiligte

• Liu, Junyu
• Perlmutter, Eric
• Rosenhaus, Vladimir
• Simmons-Duffin, David

Titel

d-dimensional SYK, AdS loops, and 6j symbols

Ist Teil von

• 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

Link zum Volltext

Quelle

EZB Electronic Journals Library

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.