The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual

By Alexei Y. Kitaev, S. J. Suh. 2017

611 citations recorded by the source corpus.

A bstractWe give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f5194a436eac9645f24766a2f73ef2453d3f7a11

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Stanford
2. Phil Saad
3. D. Harlow
4. J. Maldacena
5. S. Shenker
6. Zhenbin Yang
7. Jordan S. Cotler
8. K. Jensen

In Nuclear and High Energy Physics

1. D. Stanford
2. Phil Saad
3. Zhenbin Yang
4. S. Shenker
5. J. Maldacena
6. D. Harlow
7. Jordan S. Cotler
8. K. Jensen

Citations in the corpus

• Statistical mechanics of a two-dimensional black hole (2018, methodology): “At low temperatures, it exhibits a collective soft mode with gravity-like behavior, whose effective action involves the Schwarzian derivative, Sch ( f(x), x ) = f ′′′ f ′ − 3 2 ( f ′′ f ′ )2 [6, 8, 7].”
• Replica wormholes and the black hole interior (2019, background): “integral for long thin tubes. There is no reason to suspect that this is a problem for the current calculations, but to build condence we undertake a related calculation in the UV complete SYK model [69, 70, 71]. We will numerically nd a solution that gives a non-decaying contribution to the Renyi 2”
• JT gravity and the ensembles of random matrix theory (2019, background): “” This provides a link between JT gravity and the Sachdev-Ye-Kitaev (SYK) model [7, 8, 9], which reduces at low energies to the same Schwarzian theory [8, 9, 10].”
• The quantum gravity dynamics of near extremal black holes (2018, methodology): “les in early universe, our story might play a role and it will be interesting to study the physical consequence in that situation. Another application of our result is to connect with SYK type models [31, 32, 33, 34] since those models all have an emergent Schwarzian action at low energy. On that ac”
• A semiclassical ramp in SYK and in gravity (2018, methodology): “This is the Sachdev-Ye-Kitaev (SYK) model [12, 13, 14].”
• JT gravity as a matrix integral (2019, methodology): “This is because the low energy dynamics of the SYK model is described by the 1D Schwarzian theory [3, 7] which in turn is the boundary description of bulk 2D JT gravity [8, 9, 10].”
• Quantum chaos and the complexity of spread of states (2022, neutral): “Thus, we see that in the infinite c/β limit, where the Schwarzian theory is well described by AdS 2 [68, 72–74, 78, 79], the evolution of the TFD is well described by motion in the SL (2 , R ) group at all times, and the Hamiltonian and complexity operator (29) closes an SL (2 , R ) “complexity…”
• Notes on the complex Sachdev-Ye-Kitaev model (2019, methodology): “ boundary contribution. In an abstract sense, the bulk is an articial system that mimics most important properties of the real one. It may also be regarded as a heat bath for a small subset of sites [7]. The following argument seems to apply to all large Nsystems, but we will focus on the Majorana S”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, background): “However, one might imagine studying a similar problem in the context of an ensemble of systems, such as the SYK model [7, 8, 9, 10, 11, 12, 13, 14].”
• A theory of reparameterizations for AdS3 gravity (2018, background): “ter to be integral [6]. Here we note that if Cis indeed a multiple of 24, then the exact chiral central charge c= C+ 13 is not. Another loose end concerns an analogy with nearly AdS 2 gravity. Kitaev [100] (see also [22]) has shown that one way to arrive at the Schwarzian theory is to consider the p”
• Eternal traversable wormhole (2018, methodology): “This symmetry is explicitly broken by 1/J effects leading to a Schwarzian action [9, 8].”
• On the evolution of operator complexity beyond scrambling (2019, background): “Operator growth and the relation to thermalization has been discussed as a criterion for quantum chaos in model systems for fast scramblers, such as the SYK model [10], [11, 12].”
• 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”
• A quantum hydrodynamical description for scrambling and many-body chaos (2017, methodology): “In particular, one finds that the leading exponential growth in the expectation value of a commutator square in fact vanishes due to destructive interference, which appears to resonate well with a recent proposal regarding maximal chaos from [17, 47].”