Looking for a bulk point

Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander

doi:10.1007/JHEP01(2017)013

Title: Looking for a bulk point

Abstract

Here, we consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We also argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. Finally, we prove this statement in 1+1 dimensions by CFT methods.

Authors:

Maldacena, Juan ^[1]; Simmons-Duffin, David ^[1]; Zhiboedov, Alexander ^[2]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Harvard Univ., Cambridge, MA (United States). Center for Fundamental Laws of Nature

Publication Date:: 2017-01-03

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1360732

Grant/Contract Number:: SC0009988

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: 1; 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; Conformal Field Theory; Classical Theories of Gravity; Scattering Amplitudes

Citation Formats


                    Maldacena, Juan, Simmons-Duffin, David, and Zhiboedov, Alexander. Looking for a bulk point.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP01(2017)013.

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                    Maldacena, Juan, Simmons-Duffin, David, & Zhiboedov, Alexander. Looking for a bulk point.  United States.  https://doi.org/10.1007/JHEP01(2017)013

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                    Maldacena, Juan, Simmons-Duffin, David, and Zhiboedov, Alexander. Tue .  
"Looking for a bulk point".  United States.  https://doi.org/10.1007/JHEP01(2017)013.  https://www.osti.gov/servlets/purl/1360732.

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@article{osti_1360732,

  title        = {Looking for a bulk point},

  author       = {Maldacena, Juan and Simmons-Duffin, David and Zhiboedov, Alexander},

  abstractNote = {Here, we consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We also argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. Finally, we prove this statement in 1+1 dimensions by CFT methods.},

  doi          = {10.1007/JHEP01(2017)013},

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

  number       = 1,

  volume       = 2017,

  place        = {United States},

  year         = {2017},

  month        = {1}

}

Copy to clipboard

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Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2017, Issue 8
DOI: 10.1007/jhep08(2017)147

Analyticity in spin in conformal theories
journal, September 2017

Caron-Huot, Simon
Journal of High Energy Physics, Vol. 2017, Issue 9
DOI: 10.1007/jhep09(2017)078

Veneziano amplitude of Vasiliev theory
journal, October 2018

Turiaci, Gustavo J.; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2018, Issue 10
DOI: 10.1007/jhep10(2018)034

A conformal collider for holographic CFTs
journal, October 2018

Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2018, Issue 10
DOI: 10.1007/jhep10(2018)156

Quantum tasks in holography
journal, October 2019

May, Alex
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)233

All five-loop planar four-point functions of half-BPS operators in N = 4 $$ \mathcal{N}=4 $$ SYM
journal, November 2018

Chicherin, Dmitry; Georgoudis, Alessandro; Gonçalves, Vasco
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/jhep11(2018)069

Light-ray operators in conformal field theory
journal, November 2018

Kravchuk, Petr; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/jhep11(2018)102

Einstein gravity 3-point functions from conformal field theory
journal, December 2017

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/jhep12(2017)049

Sphere packing and quantum gravity
journal, December 2019

Hartman, Thomas; Mazáč, Dalimil; Rastelli, Leonardo
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)048

Exploring the bulk in $AdS / CFT$ : A covariant approach
journal, March 2017

Engelhardt, Netta
Physical Review D, Vol. 95, Issue 6
DOI: 10.1103/physrevd.95.066005

Boundary dual of bulk local operators
journal, July 2017

Sanches, Fabio; Weinberg, Sean J.
Physical Review D, Vol. 96, Issue 2
DOI: 10.1103/physrevd.96.026004

Loop Corrections to Supergravity on ${AdS}_{5} \times S^{5}$
journal, October 2017

Alday, Luis F.; Bissi, Agnese
Physical Review Letters, Vol. 119, Issue 17
DOI: 10.1103/physrevlett.119.171601

Handling Handles: Nonplanar Integrability in $N = 4$ Supersymmetric Yang-Mills Theory
journal, December 2018

Bargheer, Till; Caetano, João; Fleury, Thiago
Physical Review Letters, Vol. 121, Issue 23
DOI: 10.1103/physrevlett.121.231602

Quantum tasks in holography
text, January 2021

May, Alex
University of British Columbia
DOI: 10.14288/1.0401122

Einstein gravity 3-point functions from conformal field theory
text, January 2016

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
arXiv
DOI: 10.48550/arxiv.1610.09378

Hexagonalization of Correlation Functions
text, January 2016

Fleury, Thiago; Komatsu, Shota
arXiv
DOI: 10.48550/arxiv.1611.05577

Analyticity in Spin in Conformal Theories
text, January 2017

Caron-Huot, Simon
arXiv
DOI: 10.48550/arxiv.1703.00278

Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
text, January 2017

Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric
arXiv
DOI: 10.48550/arxiv.1705.02318

Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
text, January 2017

Kulaxizi, Manuela; Parnachev, Andrei; Zhiboedov, Alexander
arXiv
DOI: 10.48550/arxiv.1705.02934

All-Helicity Symbol Alphabets from Unwound Amplituhedra
text, January 2017

Prlina, Igor; Spradlin, Marcus; Stankowicz, James
arXiv
DOI: 10.48550/arxiv.1711.11507

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
text, January 2017

Prlina, Igor; Spradlin, Marcus; Stankowicz, James
arXiv
DOI: 10.48550/arxiv.1712.08049

Double-Trace Deformations of Conformal Correlations
text, January 2018

Giombi, Simone; Kirilin, Vladimir; Perlmutter, Eric
arXiv
DOI: 10.48550/arxiv.1801.01477

Light-ray operators in conformal field theory
text, January 2018

Kravchuk, Petr; Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1805.00098

A Conformal Collider for Holographic CFTs
text, January 2018

Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein
arXiv
DOI: 10.48550/arxiv.1805.07393

All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
text, January 2018

Caron-Huot, Simon; Trinh, Anh-Khoi
arXiv
DOI: 10.48550/arxiv.1809.09173

The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
preprint, January 2018

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared
arXiv
DOI: 10.48550/arxiv.1810.02436

Double copy structure of CFT correlators
text, January 2018

Farrow, Joseph A.; Lipstein, Arthur E.; McFadden, Paul
arXiv
DOI: 10.48550/arxiv.1812.11129

BMS Characters and Modular Invariance
text, January 2019

Bagchi, Arjun; Saha, Amartya
arXiv
DOI: 10.48550/arxiv.1902.07066

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Title: Looking for a bulk point

Abstract

Citation Formats

Little string amplitudes (and the unreasonable effectiveness of 6D SYM) journal, December 2014

Polynomial equations for rational conformal field theories journal, October 1988

Effects of D-instantons journal, August 1997

Causality, analyticity and an IR obstruction to UV completion journal, October 2006

Perturbative Gauge Theory as a String Theory in Twistor Space journal, October 2004

On analytic properties of vertex parts in quantum field theory journal, October 1959

Singularities in the physical region journal, July 1965

Causality constraints in conformal field theory journal, May 2016

Bootstrapping the O(N ) vector models journal, June 2014

The Amplituhedron journal, October 2014

Conformal Regge theory journal, December 2012

Borel summation of string theory for Planck scale scattering journal, August 1990

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory journal, August 1998

Stringy effects in scrambling journal, May 2015

Sewing conformal field theories II journal, December 1988

String field theory vertex from integrability journal, April 2015

Multi-instanton calculus and the AdS/CFT correspondence in superconformal field theory journal, July 1999

Gluon scattering amplitudes at strong coupling journal, June 2007

Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups journal, March 2013

Causality constraints on corrections to the graviton three-point coupling journal, February 2016

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions journal, April 2007

Eikonal methods in AdS/CFT: BFKL Pomeron at weak coupling journal, June 2008

Duality in quantum field theory journal, February 1977

The high-energy behavior of string scattering amplitudes journal, October 1987

Conformal bootstrap with slightly broken higher spin symmetry journal, June 2016

Singularities and Discontinuities of Feynman Amplitudes journal, September 1960

Global conformal invariance in quantum field theory journal, October 1975

Bootstrapping the three-loop hexagon journal, November 2011

Tensor representations of conformal algebra and conformally covariant operator product expansion journal, March 1973

Conformal partial waves and the operator product expansion journal, February 2004

Holography from conformal field theory journal, October 2009

The asymptotic behaviour of the dual pomeron amplitude journal, February 1972

Writing CFT correlation functions as AdS scattering amplitudes journal, March 2011

Conformal symmetry in two-dimensional space: Recursion representation of conformal block journal, October 1987

Construction of a crossing-simmetric, Regge-behaved amplitude for linearly rising trajectories journal, September 1968

A bound on chaos journal, August 2016

Eikonal approximation in AdS/CFT: from shock waves to four-point functions journal, August 2007

A natural language for AdS/CFT correlators journal, November 2011

Three-loop four-point correlator in N=4 SYM journal, June 2000

A universal inequality for CFT and quantum gravity journal, August 2011

A gas of D-instantons journal, July 1995

Hard Scattering and Gauge/String Duality journal, January 2002

Sewing conformal field theories I journal, December 1988

Jet evolution from weak to strong coupling journal, December 2012

Bounding scalar operator dimensions in 4 D CFT journal, December 2008

Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion journal, September 2007

Effective conformal theory and the flat-space limit of AdS journal, July 2011

Localized shocks journal, March 2015

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Unitarity and the holographic S-Matrix journal, October 2012

Infinite conformal symmetry in two-dimensional quantum field theory journal, July 1984

Simplifying instanton corrections to $ \mathcal{N} $ = 4 SYM correlators journal, April 2014

A measure of de Sitter entropy and eternal inflation journal, May 2007

Computing three-point functions for short operators journal, March 2014

Coordinate-space singularities of massless gauge theories journal, April 2014

Leading singularities and off-shell conformal integrals journal, August 2013

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude journal, September 1984

Computing three-point functions for short operators text, January 2014

Duality in Quantum Field Theory text, January 1975

Leading singularities and off-shell conformal integrals text, January 2013

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion text, January 1971

A Measure of de Sitter Entropy and Eternal Inflation text, January 2007

Holography from Conformal Field Theory text, January 2009

Classical Polylogarithms for Amplitudes and Wilson Loops text, January 2010

Effective Conformal Theory and the Flat-Space Limit of AdS text, January 2010

A Natural Language for AdS/CFT Correlators text, January 2011

Bootstrapping the three-loop hexagon text, January 2011

Conformal Regge theory text, January 2012

Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups text, January 2012

Leading singularities and off-shell conformal integrals text, January 2013

Bootstrapping the O(N) Vector Models text, January 2013

Computing Three-Point Functions for Short Operators text, January 2013

Coordinate-space singularities of massless gauge theories text, January 2013

Stringy effects in scrambling preprint, January 2014

String field theory vertex from integrability text, January 2015

A bound on chaos text, January 2015

Causality Constraints in Conformal Field Theory text, January 2015

Little string amplitudes (and the unreasonable effectiveness of 6D SYM)
journal, December 2014

Polynomial equations for rational conformal field theories
journal, October 1988

Effects of D-instantons
journal, August 1997

Causality, analyticity and an IR obstruction to UV completion
journal, October 2006

Perturbative Gauge Theory as a String Theory in Twistor Space
journal, October 2004

On analytic properties of vertex parts in quantum field theory
journal, October 1959

Singularities in the physical region
journal, July 1965

Causality constraints in conformal field theory
journal, May 2016

Bootstrapping the O(N ) vector models
journal, June 2014

The Amplituhedron
journal, October 2014

Conformal Regge theory
journal, December 2012

Borel summation of string theory for Planck scale scattering
journal, August 1990

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
journal, August 1998

Stringy effects in scrambling
journal, May 2015

Sewing conformal field theories II
journal, December 1988

String field theory vertex from integrability
journal, April 2015

Multi-instanton calculus and the AdS/CFT correspondence in superconformal field theory
journal, July 1999

Gluon scattering amplitudes at strong coupling
journal, June 2007

Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups
journal, March 2013

Causality constraints on corrections to the graviton three-point coupling
journal, February 2016

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions
journal, April 2007

Eikonal methods in AdS/CFT: BFKL Pomeron at weak coupling
journal, June 2008

Duality in quantum field theory
journal, February 1977

The high-energy behavior of string scattering amplitudes
journal, October 1987

Conformal bootstrap with slightly broken higher spin symmetry
journal, June 2016

Singularities and Discontinuities of Feynman Amplitudes
journal, September 1960

Global conformal invariance in quantum field theory
journal, October 1975

Bootstrapping the three-loop hexagon
journal, November 2011

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

Conformal partial waves and the operator product expansion
journal, February 2004

Holography from conformal field theory
journal, October 2009

The asymptotic behaviour of the dual pomeron amplitude
journal, February 1972

Writing CFT correlation functions as AdS scattering amplitudes
journal, March 2011

Conformal symmetry in two-dimensional space: Recursion representation of conformal block
journal, October 1987

Construction of a crossing-simmetric, Regge-behaved amplitude for linearly rising trajectories
journal, September 1968

A bound on chaos
journal, August 2016

Eikonal approximation in AdS/CFT: from shock waves to four-point functions
journal, August 2007

A natural language for AdS/CFT correlators
journal, November 2011

Three-loop four-point correlator in N=4 SYM
journal, June 2000

A universal inequality for CFT and quantum gravity
journal, August 2011

A gas of D-instantons
journal, July 1995

Hard Scattering and Gauge/String Duality
journal, January 2002

Sewing conformal field theories I
journal, December 1988

Jet evolution from weak to strong coupling
journal, December 2012

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion
journal, September 2007

Effective conformal theory and the flat-space limit of AdS
journal, July 2011

Localized shocks
journal, March 2015

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Unitarity and the holographic S-Matrix
journal, October 2012

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

Simplifying instanton corrections to $ \mathcal{N} $ = 4 SYM correlators
journal, April 2014

A measure of de Sitter entropy and eternal inflation
journal, May 2007

Computing three-point functions for short operators
journal, March 2014

Coordinate-space singularities of massless gauge theories
journal, April 2014

Leading singularities and off-shell conformal integrals
journal, August 2013

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude
journal, September 1984

Computing three-point functions for short operators
text, January 2014

Duality in Quantum Field Theory
text, January 1975

Leading singularities and off-shell conformal integrals
text, January 2013

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion
text, January 1971

A Measure of de Sitter Entropy and Eternal Inflation
text, January 2007

Holography from Conformal Field Theory
text, January 2009

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

Effective Conformal Theory and the Flat-Space Limit of AdS
text, January 2010

A Natural Language for AdS/CFT Correlators
text, January 2011

Bootstrapping the three-loop hexagon
text, January 2011

Conformal Regge theory
text, January 2012

Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups
text, January 2012

Leading singularities and off-shell conformal integrals
text, January 2013

Bootstrapping the O(N) Vector Models
text, January 2013

Computing Three-Point Functions for Short Operators
text, January 2013

Coordinate-space singularities of massless gauge theories
text, January 2013

Stringy effects in scrambling
preprint, January 2014

String field theory vertex from integrability
text, January 2015

A bound on chaos
text, January 2015

Causality Constraints in Conformal Field Theory
text, January 2015

Three-Loop Four-Point Correlator in N=4 SYM
text, January 2000

Perturbative Gauge Theory As A String Theory In Twistor Space
text, January 2003

Causality, Analyticity and an IR Obstruction to UV Completion
text, January 2006