Fermionic localization of the schwarzian theory

By D. Stanford, E. Witten. Journal of High Energy Physics, 2017

453 citations recorded by the source corpus.

The SYK model is a quantum mechanical model that has been proposed to be holographically dual to a 1 + 1-dimensional model of a quantum black hole. An emergent “gravitational” mode of this model is governed by an unusual action that has been called the Schwarzian action. It governs a reparametrization of a circle. We show that the path integral of the Schwarzian theory is one-loop exact. The argument uses a method of fermionic localization, even though the model itself is purely bosonic.

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

View Paper: https://www.semanticscholar.org/paper/4d06ec2aa3cc2ee592e32bf3a981e4ec69bff641

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. Zhenbin Yang
3. Phil Saad
4. S. Shenker
5. E. Witten
6. Alexei Y. Kitaev
7. D. Harlow
8. J. Maldacena

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

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

Citations in the corpus

• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, background): “Remarkably, this expression is valid even for βJ & N , when the fluctuations of the soft mode are strong [25, 27, 28].”
• A semiclassical ramp in SYK and in gravity (2018, background): “In particular, this region of the curve has an explanation involving fluctuations about the naive saddle point in the collective field description or dual AdS2 gravity theory [22, 25].”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, background): “10 (8)The “smooth” density of states may have sharp edges, as in the SYK model or JT gravity [10, 13, 43, 44, 24, 45, 21] but to leading order this does not stop the decaying behavior.”
• Asymptotic fragility, near AdS2 holography and TT¯$$ T\overline{T} $$ (2017, background): “A further independent support for the semiclassical nature of the JT gravity comes from the recent observation [32] that even before taking the flat limit the Schwarzian path integral is one loop exact.”
• Eternal traversable wormhole (2018, background): “36) was already shown to describe correctly the TFD (for η = 0) [30, 31, 32].”
• The statistical mechanics of near-BPS black holes (2020, methodology): “We review the solution given by [72] using localization and the exact spectrum derived in [69].”
• The Schwarzian theory — origins (2018, methodology): “The link between Liouville theory between branes and the geometric Alekseev-Shatashvili action is made in appendix A. Stanford and Witten showed that for a suitable choice of gauge, this becomes the standard SL(2,R) ∏ t 1/ḟ(t) measure [29].”
• Black holes and random matrices (2016, methodology): “ng it dicult to evaluate Z. In fact, with the correct measure, the theory turns out to be one-loop exact. We will present a somewhat indirect derivation of this fact. A direct proof is also possible [57]. 26 Our derivation is based on an intermediate step where we think about the SYK model for large”
• Solving the Schwarzian via the conformal bootstrap (2017, methodology): “While this is obtained in [23] by performing an inverse Laplace transform, in our approach both terms have a physical origin.”
• JT gravity as a matrix integral (2019, methodology): “A useful simplification is that both path integrals are one-loop exact [22], so we can evaluate them exactly by just doing the path integral for small fluctuations.”
• Statistical mechanics of a two-dimensional black hole (2018, methodology): “) This result was derived in several ways, in particular, by solving the SYK model in the double-scaling limit [9], by evaluating the Schwarzian path integral exactly [10], and by reducing the problem to Liouville quantum mechanics [11, 12].”
• Low-dimensional de Sitter quantum gravity (2019, methodology): “int orbit of the Virasoro group [38,43] at central charge C= 6=G 2. This measure was conjectured to be the correct one for the Schwarzian model as obtained from Jackiw-Teitelboim gravity and from SYK [44], and shown to be the right measure for nearly AdS 2 gravity in [21]. The PSL(2;R) quotient may ”
• Notes on the complex Sachdev-Ye-Kitaev model (2019, background): “The density of states (DOS) and the partition function for the pure Schwarzian model are as follows [33–36], where the energy E and the temperature β−1 are measured in units of (αSN) −1:”
• The factorization problem in Jackiw-Teitelboim gravity (2018, background): “ns Foundation \It-from-Qubit" Collaboration and the MIT Department of Physics. The work of DJ is supported in part by NSFCAREER grant PHY-1352084. 19A similar analysis was done for JT gravity in [54], where it was again observed that the result is not consistent with a thermal partition functio”
• JT gravity and the ensembles of random matrix theory (2019, methodology): “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 ”
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, background): “escribed by the Schwarzian path integral [93,94]. The Schwarzian alone is not a consistent quantum mechanics, since the path integral on the circle cannot be interpreted as Tre H for any Hamiltonian H[85,95]. This possibility arises from a quotient by residual gauge symmetries acting nontrivially on”