# Symmetries near the horizon

## Abstract

We consider a nearly-AdS_2 gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS_2 which move bulk matter relative to the dynamical boundaries. In a two-sided system, these operators satisfy an SL(2) algebra (up to non perturbative corrections). In a semiclassical limit, these generators act like SL(2) transformations of the boundary time, or conformal symmetries of the two sided boundary theory. These can be used to define an operator-state mapping. A particular large N and low temperature limit of the SYK model has precisely the same structure, and this construction of the exact generators also applies. We also discuss approximate, but simpler, constructions of the generators in the SYK model. These are closely related to the “size” operator and are connected to the maximal chaos behavior captured by out of time order correlators.

- Authors:

- Princeton Univ., NJ (United States). Dept. of Physics
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Simons Foundation

- OSTI Identifier:
- 1596665

- Grant/Contract Number:
- SC0009988; PHY-1748958

- 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: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Black Holes; Conformal Field Theory

### Citation Formats

```
Lin, Henry W., Maldacena, Juan, and Zhao, Ying. Symmetries near the horizon. United States: N. p., 2019.
Web. doi:10.1007/JHEP08(2019)049.
```

```
Lin, Henry W., Maldacena, Juan, & Zhao, Ying. Symmetries near the horizon. United States. doi:10.1007/JHEP08(2019)049.
```

```
Lin, Henry W., Maldacena, Juan, and Zhao, Ying. Thu .
"Symmetries near the horizon". United States. doi:10.1007/JHEP08(2019)049. https://www.osti.gov/servlets/purl/1596665.
```

```
@article{osti_1596665,
```

title = {Symmetries near the horizon},

author = {Lin, Henry W. and Maldacena, Juan and Zhao, Ying},

abstractNote = {We consider a nearly-AdS_2 gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS_2 which move bulk matter relative to the dynamical boundaries. In a two-sided system, these operators satisfy an SL(2) algebra (up to non perturbative corrections). In a semiclassical limit, these generators act like SL(2) transformations of the boundary time, or conformal symmetries of the two sided boundary theory. These can be used to define an operator-state mapping. A particular large N and low temperature limit of the SYK model has precisely the same structure, and this construction of the exact generators also applies. We also discuss approximate, but simpler, constructions of the generators in the SYK model. These are closely related to the “size” operator and are connected to the maximal chaos behavior captured by out of time order correlators.},

doi = {10.1007/JHEP08(2019)049},

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

number = 8,

volume = 2019,

place = {United States},

year = {2019},

month = {8}

}

Works referenced in this record:

##
Diving into traversable wormholes: Diving into traversable wormholes

journal, May 2017

- Maldacena, Juan; Stanford, Douglas; Yang, Zhenbin
- Fortschritte der Physik, Vol. 65, Issue 5

##
Construction of bulk fields with gauge redundancy

journal, September 2012

- Heemskerk, Idse
- Journal of High Energy Physics, Vol. 2012, Issue 9

##
Sachdev–Ye–Kitaev model as Liouville quantum mechanics

journal, October 2016

- Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
- Nuclear Physics B, Vol. 911

##
Solving the Schwarzian via the conformal bootstrap

journal, August 2017

- Mertens, Thomas G.; Turiaci, Gustavo J.; Verlinde, Herman L.
- Journal of High Energy Physics, Vol. 2017, Issue 8

##
Addendum to computational complexity and black hole horizons: Addendum to computational complexity and black hole horizons

journal, January 2016

- Susskind, Leonard
- Fortschritte der Physik, Vol. 64, Issue 1

##
Models of AdS2 backreaction and holography

journal, November 2015

- Almheiri, Ahmed; Polchinski, Joseph
- Journal of High Energy Physics, Vol. 2015, Issue 11

##
Power-law out of time order correlation functions in the SYK model

journal, August 2017

- Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
- Nuclear Physics B, Vol. 921

##
An investigation of AdS2 backreaction and holography

journal, July 2016

- Engelsöy, Julius; Mertens, Thomas G.; Verlinde, Herman
- Journal of High Energy Physics, Vol. 2016, Issue 7

##
The bulk dual of SYK: cubic couplings

journal, May 2017

- Gross, David J.; Rosenhaus, Vladimir
- Journal of High Energy Physics, Vol. 2017, Issue 5

##
Operator growth in the SYK model

journal, June 2018

- Roberts, Daniel A.; Stanford, Douglas; Streicher, Alexandre
- Journal of High Energy Physics, Vol. 2018, Issue 6

##
Bulk and transhorizon measurements in AdS/CFT

journal, October 2012

- Heemskerk, Idse; Marolf, Donald; Polchinski, Joseph
- Journal of High Energy Physics, Vol. 2012, Issue 10

##
Towards a derivation of holographic entanglement entropy

journal, May 2011

- Casini, Horacio; Huerta, Marina; Myers, Robert C.
- Journal of High Energy Physics, Vol. 2011, Issue 5

##
Entanglement entropy and nonabelian gauge symmetry

journal, October 2014

- Donnelly, William
- Classical and Quantum Gravity, Vol. 31, Issue 21

##
Chaos in ${\mathrm{AdS}}_{2}$ Holography

journal, September 2016

- Jensen, Kristan
- Physical Review Letters, Vol. 117, Issue 11

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

journal, May 2018

- Kitaev, Alexei; Suh, S. Josephine
- Journal of High Energy Physics, Vol. 2018, Issue 5

##
Gravitation and hamiltonian structure in two spacetime dimensions

journal, June 1983

- Teitelboim, Claudio
- Physics Letters B, Vol. 126, Issue 1-2

##
Traversable wormholes via a double trace deformation

journal, December 2017

- Gao, Ping; Jafferis, Daniel Louis; Wall, Aron C.
- Journal of High Energy Physics, Vol. 2017, Issue 12

##
Fast scramblers

journal, October 2008

- Sekino, Yasuhiro; Susskind, L.
- Journal of High Energy Physics, Vol. 2008, Issue 10