Generalized conformal structure, dilaton gravity and SYK

Abstract

A theory admits generalized conformal structure if the only scale in the quantum theory is set by a dimensionful coupling. SYK is an example of a theory with generalized conformal structure and in this paper we investigate the consequences of this structure for correlation functions and for the holographic realization of SYK. The Ward identities associated with the generalized conformal structure of SYK are implemented holographically in gravity/multiple scalar theories, which always have a parent AdS 3 origin. For questions involving only the graviton/running scalar sector, one can always describe the bulk running in terms of a single scalar but multiple running scalars are in general needed once one includes the bulk fields corresponding to all SYK operators. We then explore chaos in holographic theories with generalized conformal structure. The four point function explored by Maldacena, Shenker and Stanford exhibits exactly the same chaotic behaviour in any such theory as in holographic realizations of conformal theories i.e. the dimensionful coupling scale does not affect the chaotic exponential growth.

An introduction to the SYK model

“…As a result of the SL 2 (R) isometry of AdS 2 , any correlation function of the φ n , at points extrapolated to the boundary of AdS 2 , will take 14 In fact, similar ladder diagrams appear in the fishnet theory, a deformation of N = 4 super Yang-Mills [53]. 15 For further studies of two-dimensional gravity, AdS 2 , and the Schwarzian, see [58][59][60][61][62][63][64][65][66][67]. clockwise circles enclosing the positive even integers h = 2n.…”

5D rotating black holes and the nAdS2/nCFT1 correspondence

“…in [8]. Different generalizations of the Jackiw-Teitelboim model were obtained recently via Kaluza-Klein reduction from a higher dimensional theory in [15,[20][21][22][38][39][40]. In comparisons with work on 2D dilaton gravity it may be useful to identify ψ as "the" dilaton field.…”

Space-time in the SYK model

“…For the SYK model the IR and the near-IR limit are solvable, with evaluations [2,6,8] of the invariant Schwarzian action representing the boundary Gravity degrees of freedom possibly related to JT type [81,82] dual theory [83][84][85][86][87] (See also [88][89][90][91][92][93][94][95][96][97]). …”