The Schwarzian theory — origins

By Tom Mertens. 2018

166 citations recorded by the source corpus.

A bstractIn this paper we further study the 1d Schwarzian theory, the universal low-energy limit of Sachdev-Ye-Kitaev models, using the link with 2d Liouville theory. We provide a path-integral derivation of the structural link between both theories, and study the relation between 3d gravity, 2d Jackiw-Teitelboim gravity, 2d Liouville and the 1d Schwarzian. We then generalize the Schwarzian double-scaling limit to rational models, relevant for SYK-type models with internal symmetries. We identify the holographic gauge theory as a 2d BF theory and compute correlators of the holographically dual 1d particle-on-a-group action, decomposing these into diagrammatic building blocks, in a manner very similar to the Schwarzian theory.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8fb2f8d0678ef78ed35cea7d634ebd0c18fe65ec

How researchers see this paper

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

In Geometry and Topology

1. G. Turiaci
2. Zhenbin Yang
3. K. Jensen
4. Jordan S. Cotler
5. A. Maloney
6. M. Berkooz
7. Phil Saad
8. E. Witten

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

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

Citations in the corpus

• JT gravity and the ensembles of random matrix theory (2019, background): “The contribution of a particular topology to the path (1)This has included many different derivations of the exact path integral [12, 13, 14, 15, 16, 17, 18, 19, 20], studies of the Hilbert space structure [21, 18, 22, 23], correlation functions [24, 25, 26], the physical symmetry charges [27], and ”
• Low-dimensional de Sitter quantum gravity (2019, background): “imensional groups and their quantization provide a unied description of the boundary models for nearly dS 2 and dS 3 gravity obtained in this work, as well as for nearly AdS 2 and pure AdS 3 gravity [36,44,81,126]. In these settings the gravitational dynamics has no bulk modes, only having boundary ”
• Towards a full solution of the large N double-scaled SYK model (2018, methodology): “In this section we work out these diagrammatic rules, in analogy to what was done in [28, 29, 36, 37] for the Schwarzian theory.”
• A theory of reparameterizations for AdS3 gravity (2018, background): “path integral methods throughout.1 We also note that other authors have recently stated in words that a more careful version of the analysis of [10] leads to the boundary model (1.4) { see especially [14,15]. However to our knowledge we are the rst to give a path integral derivation of the boundary ”
• The statistical mechanics of near-BPS black holes (2020, background): “We also keep the left-moving SU(2) chemical potential α fixed in this limit, and consider zero right-moving If extra currents are present, they are easy to take into account and in the near-extremal limit looking at states where their charge is fixed, their fluctuations are frozen (this can be deriv”
• JT gravity as a matrix integral (2019, background): “The analogous statement for BF theory with Lie group G is that the boundary theory is the quantum mechanics of a particle moving on the G manifold [89].”
• The quantum gravity dynamics of near extremal black holes (2018, result): “This reproduces what was found in [6, 7, 44] by other methods.”