All point correlation functions in SYK
By D. Gross, V. Rosenhaus. 2017
165 citations recorded by the source corpus.
A bstractLarge N melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together. We uncover an incredibly useful property of these theories: the six-point function, or equivalently, the three-point function of the primary O(N ) invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions, to leading nontrivial order in 1/N , through simple Feynman-like rules. The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point functions. We explicitly calculate the bilinear three-point function for q-body SYK, at any q. This leads to the bilinear four-point function, as well as all higher-point functions, expressed in terms of higher-point conformal blocks, which we discuss. We find universality of correlators of operators of large dimension, which we simplify through a saddle point analysis. We comment on the implications for the AdS dual of SYK.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/3ad7d7e202c56853b2b23650023c31ae8493ea05
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In Astronomy and Astrophysics
- M. Berkooz
- Phil Saad
- V. Rosenhaus
- Tom Mertens
- Genís Torrents
- Mikhail Isachenkov
- Vladimir Narovlansky
- E. Witten
In Nuclear and High Energy Physics
- Phil Saad
- M. Berkooz
- Genís Torrents
- Mikhail Isachenkov
- Vladimir Narovlansky
- Tom Mertens
- V. Rosenhaus
- E. Witten
Citations in the corpus
- The Schwarzian theory — origins (2018, background): “Sachdev-Ye-Kitaev (SYK) models of N Majorana fermions with random all-to-all interactions have received a host of attention in the past few years [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], mainly due to the appearance of maximally chaotic behavior [13, 14, 15, 16, 17], suggesting a 2d holographic dual”
- Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, background): “(3)Correlation functions in JT gravity have been studied in [20, 21, 22, 23, 24, 25, 26, 27, 28].”
- Towards a full solution of the large N double-scaled SYK model (2018, methodology): “also theories with similar behavior to SYK, but without disorder [16{18]. The relation of SYK to random matrix theory was discussed in { 1 { [19,20]. Higher correlation functions were studied as well [21,22], and results beyond the leading order in Nwere obtained [23{25]. One usually studies the SYK”
- An introduction to the SYK model (2018, methodology): “es of the Schwarzian, see [33{40], as well as references in Sec. 5.1, regarding dilaton gravity. 4.Correlation Functions We now turn to higher point correlation functions, following the discussion in [41]. The four-point function, like the two-point function, is given by the solution of an integral ”