The AdS_{3} propagator and the fate of locality
Abstract
We recently used Virasoro symmetry considerations to propose an exact formula for a bulk protofield φ in AdS_{3}. In this paper we study the propagator . We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and welldefined at long distances, its perturbative expansion in ${G}_{N}=\frac{3}{2c}$ exhibits UV/IR mixing effects. If we nevertheless interpret as a probe of bulk locality, then when ${G}_{N{m}_{\varphi}}\ll 1$ locality breaks down at the new shortdistance scale ${\sigma}_{\ast}\sim \sqrt[4]{{G}_{N}{R}_{\mathrm{A}\mathrm{d}\mathrm{S}}^{3}}$. For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from nonperturbative quantum gravitational effects.
 Authors:

 Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
 Boston Univ., MA (United States). Dept. of Physics
 Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy; Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP); Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
 Publication Date:
 Research Org.:
 Boston Univ., MA (United States); Johns Hopkins Univ., Baltimore, MD (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
 OSTI Identifier:
 1501934
 Grant/Contract Number:
 SC0010025; PHY1454083
 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: 2018; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdSCFT correspondence; conformal and W Symmetry; conformal field theory; models of quantum gravity
Citation Formats
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, and Li, Daliang. The AdS3 propagator and the fate of locality. United States: N. p., 2018.
Web. doi:10.1007/jhep04(2018)075.
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, & Li, Daliang. The AdS3 propagator and the fate of locality. United States. doi:10.1007/jhep04(2018)075.
Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, and Li, Daliang. Fri .
"The AdS3 propagator and the fate of locality". United States. doi:10.1007/jhep04(2018)075. https://www.osti.gov/servlets/purl/1501934.
@article{osti_1501934,
title = {The AdS3 propagator and the fate of locality},
author = {Chen, Hongbin and Fitzpatrick, A. Liam and Kaplan, Jared and Li, Daliang},
abstractNote = {We recently used Virasoro symmetry considerations to propose an exact formula for a bulk protofield φ in AdS3. In this paper we study the propagator . We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and welldefined at long distances, its perturbative expansion in G N = 3 2 c exhibits UV/IR mixing effects. If we nevertheless interpret as a probe of bulk locality, then when G N m ϕ ≪ 1 locality breaks down at the new shortdistance scale σ ∗ ∼ G N R A d S 3 4 . For φ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from nonperturbative quantum gravitational effects.},
doi = {10.1007/jhep04(2018)075},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}
Web of Science
Works referenced in this record:
Quantum Theory of Gravity. I. The Canonical Theory
journal, August 1967
 DeWitt, Bryce S.
 Physical Review, Vol. 160, Issue 5
On the construction of charged operators inside an eternal black hole
journal, January 2017
 Guica, Monica; Jafferis, Daniel
 SciPost Physics, Vol. 3, Issue 2
Virasoro conformal blocks and thermality from classical background fields
journal, November 2015
 Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
 Journal of High Energy Physics, Vol. 2015, Issue 11
Time evolution of entanglement entropy from a pulse
journal, December 2012
 Roberts, Matthew M.
 Journal of High Energy Physics, Vol. 2012, Issue 12
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
Virasoro conformal blocks in closed form
journal, August 2015
 Perlmutter, Eric
 Journal of High Energy Physics, Vol. 2015, Issue 8
Conformal blocks beyond the semiclassical limit
journal, May 2016
 Fitzpatrick, A. Liam; Kaplan, Jared
 Journal of High Energy Physics, Vol. 2016, Issue 5
Universality of longdistance AdS physics from the CFT bootstrap
journal, August 2014
 Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
 Journal of High Energy Physics, Vol. 2014, Issue 8
Conformal symmetry in twodimensional space: Recursion representation of conformal block
journal, October 1987
 Zamolodchikov, Al. B.
 Theoretical and Mathematical Physics, Vol. 73, Issue 1
Causality constraints in conformal field theory
journal, May 2016
 Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
 Journal of High Energy Physics, Vol. 2016, Issue 5
Creating a (Quantum?) Constraint, in Pre Planckian SpaceTime Early Universe via the Einstein Cosmological Constant in a One to One and Onto Comparison between Two Action Integrals
journal, January 2017
 Beckwith, Andrew Walcott
 Journal of High Energy Physics, Gravitation and Cosmology, Vol. 03, Issue 02
One loop tests of higher spin AdS/CFT
journal, December 2013
 Giombi, Simone; Klebanov, Igor R.
 Journal of High Energy Physics, Vol. 2013, Issue 12
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
An exact operator that knows its location
journal, February 2018
 Anand, N.; Chen, Hongbin; Fitzpatrick, A. Liam
 Journal of High Energy Physics, Vol. 2018, Issue 2
Gauge theory correlators from noncritical string theory
journal, May 1998
 Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
 Physics Letters B, Vol. 428, Issue 12
On information loss in AdS3/CFT2
journal, May 2016
 Fitzpatrick, A. Liam; Kaplan, Jared; Li, Daliang
 Journal of High Energy Physics, Vol. 2016, Issue 5
Black hole collapse in the 1/c expansion
journal, July 2016
 Anous, Tarek; Hartman, Thomas; Rovai, Antonin
 Journal of High Energy Physics, Vol. 2016, Issue 7
Integrability and blackhole microstate geometries
journal, November 2017
 Bena, Iosif; Turton, David; Walker, Robert
 Journal of High Energy Physics, Vol. 2017, Issue 11
An infalling observer in AdS/CFT
journal, October 2013
 Papadodimas, Kyriakos; Raju, Suvrat
 Journal of High Energy Physics, Vol. 2013, Issue 10
Bulk locality and quantum error correction in AdS/CFT
journal, April 2015
 Almheiri, Ahmed; Dong, Xi; Harlow, Daniel
 Journal of High Energy Physics, Vol. 2015, Issue 4
Anti de Sitter space and holography
journal, January 1998
 Witten, Edward
 Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
Analytic continuation of Liouville theory
journal, December 2011
 Harlow, Daniel; Maltz, Jonathan; Witten, Edward
 Journal of High Energy Physics, Vol. 2011, Issue 12
Bulk local states and crosscaps in holographic CFT
journal, October 2016
 Nakayama, Yu; Ooguri, Hirosi
 Journal of High Energy Physics, Vol. 2016, Issue 10
A stereoscopic look into the bulk
journal, July 2016
 Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel
 Journal of High Energy Physics, Vol. 2016, Issue 7
Exact Virasoro blocks from Wilson lines and backgroundindependent operators
journal, July 2017
 Fitzpatrick, A. Liam; Kaplan, Jared; Li, Daliang
 Journal of High Energy Physics, Vol. 2017, Issue 7
Bulk locality from modular flow
journal, July 2017
 Faulkner, Thomas; Lewkowycz, Aitor
 Journal of High Energy Physics, Vol. 2017, Issue 7
Typicality versus thermality: an analytic distinction
journal, February 2008
 Balasubramanian, Vijay; Czech, Bartłomiej; Hubeny, Veronika E.
 General Relativity and Gravitation, Vol. 40, Issue 9
Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016
 Hijano, Eliot; Kraus, Per; Perlmutter, Eric
 Journal of High Energy Physics, Vol. 2016, Issue 1
Threedimensional quantum geometry and black holes
conference, January 1999
 Bañados, Máximo
 The second meeting on trends in theoretical physics, AIP Conference Proceedings
Infinite conformal symmetry in twodimensional quantum field theory
journal, July 1984
 Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B.
 Nuclear Physics B, Vol. 241, Issue 2
Tidal stresses and energy gaps in microstate geometries
journal, February 2018
 Tyukov, Alexander; Walker, Robert; Warner, Nicholas P.
 Journal of High Energy Physics, Vol. 2018, Issue 2
Bulk equations of motion from CFT correlators
journal, September 2015
 Kabat, Daniel; Lifschytz, Gilad
 Journal of High Energy Physics, Vol. 2015, Issue 9
Global conformal invariance in quantum field theory
journal, October 1975
 Lüscher, M.; Mack, G.
 Communications in Mathematical Physics, Vol. 41, Issue 3
A numerical approach to Virasoro blocks and the information paradox
journal, September 2017
 Chen, Hongbin; Hussong, Charles; Kaplan, Jared
 Journal of High Energy Physics, Vol. 2017, Issue 9
Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude
journal, September 1984
 Zamolodchikov, Al. B.
 Communications in Mathematical Physics, Vol. 96, Issue 3
Locality, bulk equations of motion and the conformal bootstrap
journal, October 2016
 Kabat, Daniel; Lifschytz, Gilad
 Journal of High Energy Physics, Vol. 2016, Issue 10
AdS/CFT fourpoint functions: How to succeed at zintegrals without really trying
journal, November 1999
 D'Hoker, Eric; Freedman, Daniel Z.; Rastelli, Leonardo
 Nuclear Physics B, Vol. 562, Issue 12
Bulk locality and boundary creating operators
journal, October 2015
 Nakayama, Yu; Ooguri, Hirosi
 Journal of High Energy Physics, Vol. 2015, Issue 10
A CFT perspective on gravitational dressing and bulk locality
journal, January 2017
 Lewkowycz, Aitor; Turiaci, Gustavo J.; Verlinde, Herman
 Journal of High Energy Physics, Vol. 2017, Issue 1
Works referencing / citing this record:
The bulktoboundary propagator in black hole microstate backgrounds
journal, June 2019
 Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared
 Journal of High Energy Physics, Vol. 2019, Issue 6
AdS3 reconstruction with general gravitational dressings
journal, July 2019
 Chen, Hongbin; Kaplan, Jared; Sharma, Utkarsh
 Journal of High Energy Physics, Vol. 2019, Issue 7
Universal lowesttwist in CFTs from holography
journal, August 2019
 Fitzpatrick, A. Liam; Huang, KuoWei
 Journal of High Energy Physics, Vol. 2019, Issue 8
Note on bulk reconstruction in ${\mathrm{AdS}}_{3}/\mathrm{warped}$ ${\mathrm{CFT}}_{2}$
journal, October 2019
 Lin, Yuhan; Chen, Bin
 Physical Review D, Vol. 100, Issue 8