A semiclassical ramp in SYK and in gravity

By Phil Saad, S. Shenker, D. Stanford. 2018

382 citations recorded by the source corpus.

In finite entropy systems, real-time partition functions do not decay to zero at late time. Instead, assuming random matrix universality, suitable averages exhibit a growing "ramp" and "plateau" structure. Deriving this non-decaying behavior in a large $N$ collective field description is a challenge related to one version of the black hole information problem. We describe a candidate semiclassical explanation of the ramp for the SYK model and for black holes. In SYK, this is a two-replica nonperturbative saddle point for the large $N$ collective fields, with zero action and a compact zero mode that leads to a linearly growing ramp. In the black hole context, the solution is a two-sided black hole that is periodically identified under a Killing time translation. We discuss but do not resolve some puzzles that arise.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/39a1bb2c3d94a00f044b7fbc6657cb58cf5f288e

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

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

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

1. D. Stanford
2. Phil Saad
3. S. Shenker
4. Jordan S. Cotler
5. K. Jensen
6. J. Maldacena
7. Henry Maxfield
8. S. Raju

Citations in the corpus

• Bra-ket wormholes in gravitationally prepared states (2020, background): “onsible for the \ramp" in the time dependence of the spectral form factor in SYK-like theories, see gure23. It is, however, not identical because in their case the bulk theory is AdS 2. Also, in [31], the parameter analogous to T xis the black hole temperature and it is natural to x it (or simi”
• The quantum gravity dynamics of near extremal black holes (2018, background): “hen approaches e23S 0, the partition function becomes less than one and denitely at this time scale we need new physics. A recently study of gravitational physics at this time scale was discussed in [22]. 7 Conclusion Our result gives an explicit formula (6.74) to calculate all order corrections to ”
• The Page curve of Hawking radiation from semiclassical geometry (2019, background): “They are also likely to involve other topologies, as in the long time discussion in [44, 45].”
• A theory of reparameterizations for AdS3 gravity (2018, neutral): “1.4) subject to a single (rather than a doubled) PSL(2;R) quotient. This result paves the way for future discussions [20] of traversable wormholes [21,22] and perhaps even a semiclassical \ramp" [23,24] in AdS 3 gravity using this boundary eld theory. There are two other comments in order. The ”
• Replica wormholes and the black hole interior (2019, methodology): “ non-averaged decoupled systems could be ruled out because they are not actual saddle points. However, in JT gravity, the wormhole describing the ramp is a saddle point in the microcanonical ensemble [24, 26]. We see no obstruction to the existence of such microcanonically stable wormholes in more c”
• JT gravity and the ensembles of random matrix theory (2019, background): “Further work has included generalizations to include higher spin fields [29], supersymmetry [30], different topologies [31, 32, 23, 26], and de Sitter space [33, 34].”
• Two dimensional nearly de Sitter gravity (2019, neutral): “It has been mostly studied with negative curvature, see eg [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26].”
• AdS3 gravity and random CFT (2020, methodology): “this sense that JT gravity is dual to a certain matrix ensemble. A striking feature of JT gravity is that it includes a sum over wormhole geometries which smoothly connect multiple asymptotic regions [7,12]. For example, in the genus expansion, the path integral with two boundaries is in pictures gi”
• JT gravity as a matrix integral (2019, methodology): “This, as well as other hints described in [13], led us to study JT gravity on surfaces of arbitrary topology.”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “5) (20)In [14] only the saddle point geometry was considered, so this was not important.”
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, background): “ional gravity. Indeed, the model described in section3.1is plausibly the simplest possible such theory. Our models are inspired by recent work studying spacetimes of nontrivial topology in JT gravity [62,86,87], along with the addition of ‘end-of-the-world brane’ dynamical boundaries [49]. We furthe”
• Onset of random matrix behavior in scrambling systems (2018, methodology): “(37)The methods being used in [70] should be helpful.”
• A Note On Complex Spacetime Metrics (2021, neutral): “This rather singular spacetime has a rather simple regularization, essentially discussed in [21], in which we avoid letting r pass through the origin in the complex plane.”
• Low-dimensional de Sitter quantum gravity (2019, background): “ future and past boundary. In fact we may reinterpret global dS 2 as the \double trumpet" geometry of [21], whose analytic continuation computes the semiclassical ramp of nearly AdS 2 gravity in [35]. This double trumpet is a topological annulus described by the metric ds02 = dˆ2 + b2 cosh2 ˆd2”