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.

42 pages, 3 figures

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Cited by in corpus (17)

• An introduction to the SYK model
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Three Dimensional View of Arbitrary $q$ SYK models
• $Ad{S}_2$ dilaton gravity from reductions of some nonrelativistic theories
• On aspects of 2-dim dilaton gravity, dimensional reduction and holography
• Topological Sachdev-Ye-Kitaev Model
• Rotating Black Holes in AdS, Extremality and Chaos
• JT gravity and the models of Hawking-Page transition for 2D black holes
• Exact Embeddings of JT Gravity in Strings and M-theory
• Gravitational Anomalies in nAdS${}_2$/nCFT${}_1$
• Topology of black hole phase transition in JT gravity
• Models of phase stability in Jackiw-Teitelboim gravity
• Near Conformal Perturbation Theory in SYK Type Models
• SYK/AdS duality with Yang-Baxter deformations
• Holographic Aspects of Even-Dimensional Topological Gravity
• AdS black holes in two-dimensional dilaton gravity and holography