Fermionic localization of the schwarzian theory

Stanford, Douglas; Witten, Edward

doi:10.1007/JHEP10(2017)008

Title: Fermionic localization of the schwarzian theory

Abstract

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. Here, the argument uses a method of fermionic localization, even though the model itself is purely bosonic.

Authors:

Stanford, Douglas ^[1]; Witten, Edward ^[1]

Institute for Advanced Study, Princeton, NJ (United States)

Publication Date:: Mon Oct 02 00:00:00 EDT 2017

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1414835

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Field Theories in Lower Dimensions; Nonperturbative Effects

Citation Formats


                    Stanford, Douglas, and Witten, Edward. Fermionic localization of the schwarzian theory.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP10(2017)008.

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                    Stanford, Douglas, & Witten, Edward. Fermionic localization of the schwarzian theory.  United States.  https://doi.org/10.1007/JHEP10(2017)008

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                    Stanford, Douglas, and Witten, Edward. Mon .  
"Fermionic localization of the schwarzian theory".  United States.  https://doi.org/10.1007/JHEP10(2017)008.  https://www.osti.gov/servlets/purl/1414835.

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@article{osti_1414835,

  title        = {Fermionic localization of the schwarzian theory},

  author       = {Stanford, Douglas and Witten, Edward},

  abstractNote = {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. Here, the argument uses a method of fermionic localization, even though the model itself is purely bosonic.},

  doi          = {10.1007/JHEP10(2017)008},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2017,

  place        = {United States},

  year         = {Mon Oct 02 00:00:00 EDT 2017},

  month        = {Mon Oct 02 00:00:00 EDT 2017}

}

Copy to clipboard

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Title: Fermionic localization of the schwarzian theory

Abstract

Citation Formats

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Sachdev–Ye–Kitaev model as Liouville quantum mechanics journal, October 2016

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An investigation of AdS2 backreaction and holography journal, July 2016

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Orbits of diff S1 in the space of quadratic differentials journal, March 1989

Models of AdS2 backreaction and holography journal, November 2015

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Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity journal, September 1989

Orbits of the group of diffeomorphisms of a circle and local Lie superalgebras journal, January 1981

The propagator for quantum mechanics on a group manifold from an infinite-dimensional analogue of the Duistermaat-Heckman integration formula journal, July 1989

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Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories journal, April 1995

Conformal invariance, the KdV equation and coadjoint orbits of the Virasoro algebra journal, May 1988

The moment map and equivariant cohomology journal, January 1984

Coadjoint orbits of the Virasoro group journal, March 1988

The Moment Map and Equivariant Cohomology book, January 1995

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A Generalization of Sachdev-Ye-Kitaev text, January 2016

Black Holes and Random Matrices text, January 2016

Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet text, January 1992

Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories text, January 1994

Localization and non-renormalization in Chern-Simons theory journal, January 2019

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Towards a bulk description of higher spin SYK journal, May 2018

Note on global symmetry and SYK model journal, May 2019

Statistical mechanics of a two-dimensional black hole journal, May 2019

Shockwave S-matrix from Schwarzian quantum mechanics journal, November 2018

Jackiw-Teitelboim gravity and rotating black holes journal, November 2019

Universal low temperature theory of charged black holes with AdS 2 horizons journal, May 2019

Geometric actions for three-dimensional gravity journal, December 2017

An introduction to the SYK model journal, July 2019

Conformality of 1 / N corrections in Sachdev-Ye-Kitaev-like models journal, December 2019

Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino journal, July 2018

Unusual view of the Schwarzian theory journal, December 2018

Two-dimensional dilaton gravity theory and lattice Schwarzian theory journal, October 2019

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Supersymmetric SYK Model with Global Symmetry text, January 2017

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The Schwarzian Theory - Origins text, January 2018

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On the variation in the cohomology of the symplectic form of the reduced phase space
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Super Coadjoint Orbits of the N = 2 super-Virasoro Group
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Sachdev–Ye–Kitaev model as Liouville quantum mechanics
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Power-law out of time order correlation functions in the SYK model
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Localization for nonabelian group actions
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Seiberg-Witten Prepotential from Instanton Counting
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The Method of Coadjoint Orbits: an Algorithm for the Construction of Invariant Actions
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Chaos in ${AdS}_{2}$ Holography
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Gravitation and hamiltonian structure in two spacetime dimensions
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Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
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Gapless spin-fluid ground state in a random quantum Heisenberg magnet
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Orbits of diff S1 in the space of quadratic differentials
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Models of AdS2 backreaction and holography
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Localization formulas, superconnections, and the index theorem for families
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Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity
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Orbits of the group of diffeomorphisms of a circle and local Lie superalgebras
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The propagator for quantum mechanics on a group manifold from an infinite-dimensional analogue of the Duistermaat-Heckman integration formula
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The moment map and equivariant cohomology
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Coadjoint orbits of the Virasoro group
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A Generalization of Sachdev-Ye-Kitaev
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Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
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JT gravity, KdV equations and macroscopic loop operators
journal, January 2020

Nearly AdS2 holography in quantum CGHS model
journal, January 2020

Towards a bulk description of higher spin SYK
journal, May 2018

Note on global symmetry and SYK model
journal, May 2019

Statistical mechanics of a two-dimensional black hole
journal, May 2019

Shockwave S-matrix from Schwarzian quantum mechanics
journal, November 2018

Jackiw-Teitelboim gravity and rotating black holes
journal, November 2019

Universal low temperature theory of charged black holes with AdS ₂ horizons
journal, May 2019

Geometric actions for three-dimensional gravity
journal, December 2017

An introduction to the SYK model
journal, July 2019

Conformality of $1 / N$ corrections in Sachdev-Ye-Kitaev-like models
journal, December 2019

Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino
journal, July 2018

Unusual view of the Schwarzian theory
journal, December 2018

Two-dimensional dilaton gravity theory and lattice Schwarzian theory
journal, October 2019

Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino
book, May 2018

Notes on Melonic $O(N)^{q-1}$ Tensor Models
text, January 2017

Supersymmetric SYK Model with Global Symmetry
text, January 2017

Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
text, January 2018

The Schwarzian Theory - Origins
text, January 2018

Towards a bulk description of higher spin SYK
text, January 2018

Localization and Non-Renormalization in Chern-Simons Theory
text, January 2018

The Schwarzian Theory - A Wilson Line Perspective
text, January 2018

On Melonic Supertensor Models
text, January 2018

Quantum Computation as Gravity
text, January 2018

A theory of reparameterizations for AdS$_3$ gravity
text, January 2018

The Quantum Gravity Dynamics of Near Extremal Black Holes
text, January 2018

Quantum Quenches and Thermalization in SYK models
text, January 2018

Universal low temperature theory of charged black holes with AdS$_2$ horizons
text, January 2019

Integrable and chaotic dynamics of spins coupled to an optical cavity
text, January 2019

An exact quantization of Jackiw-Teitelboim gravity
text, January 2019

The Scales of Black Holes with nAdS$_2$ Geometry
text, January 2019

Nearly AdS$_2$ holography in quantum CGHS model
text, January 2019