Holographic reconstruction of AdS exchanges from crossing symmetry

Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric

doi:10.1007/JHEP08(2017)147

Title: Holographic reconstruction of AdS exchanges from crossing symmetry

Abstract

Motivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a single-trace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum four-point function (OOOO) as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in 1/N. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS₅. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections at finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist τ and spin s, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators [OO]_n,ℓ. We find that the double-trace anomalous dimensions γ _n,ℓ are negative, monotonic and convex functions of ℓ, for all n and all ℓ > s. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the “derivative relation” between double-trace anomalous dimensions andmore »« less

Authors:

Alday, Luis F. ^[1]; Bissi, Agnese ^[2]; Perlmutter, Eric ^[3]

Univ. of Oxford (United Kingdom). Mathematical Inst.
Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
Princeton Univ., NJ (United States). Dept. of Physics

Publication Date:: Thu Aug 31 00:00:00 EDT 2017

Research Org.:: Princeton Univ., NJ (United States); Univ. of Oxford (United Kingdom); Harvard Univ., Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC)

OSTI Identifier:: 1425403

Grant/Contract Number:: FG02-91ER40671; 306260

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: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 1/N expansion; conformal and W symmetry; conformal field theory

Citation Formats


                    Alday, Luis F., Bissi, Agnese, and Perlmutter, Eric. Holographic reconstruction of AdS exchanges from crossing symmetry.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP08(2017)147.

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                    Alday, Luis F., Bissi, Agnese, & Perlmutter, Eric. Holographic reconstruction of AdS exchanges from crossing symmetry.  United States.  https://doi.org/10.1007/JHEP08(2017)147

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                    Alday, Luis F., Bissi, Agnese, and Perlmutter, Eric. Thu .  
"Holographic reconstruction of AdS exchanges from crossing symmetry".  United States.  https://doi.org/10.1007/JHEP08(2017)147.  https://www.osti.gov/servlets/purl/1425403.

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@article{osti_1425403,

  title        = {Holographic reconstruction of AdS exchanges from crossing symmetry},

  author       = {Alday, Luis F. and Bissi, Agnese and Perlmutter, Eric},

  abstractNote = {Motivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a single-trace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum four-point function (OOOO) as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in 1/N. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS5. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections at finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist τ and spin s, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators [OO]n,ℓ. We find that the double-trace anomalous dimensions γ n,ℓ are negative, monotonic and convex functions of ℓ, for all n and all ℓ > s. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the “derivative relation” between double-trace anomalous dimensions and OPE coefficients does not hold in general, and derive the explicit form of the deviation in several cases. Finally, we study large n limits of γ n,ℓ, relevant for the Regge and bulk-point regimes.},

  doi          = {10.1007/JHEP08(2017)147},

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

  number       = 8,

  volume       = 2017,

  place        = {United States},

  year         = {Thu Aug 31 00:00:00 EDT 2017},

  month        = {Thu Aug 31 00:00:00 EDT 2017}

}

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Title: Holographic reconstruction of AdS exchanges from crossing symmetry

Abstract

Citation Formats

Aspects of superconformal field theories in six dimensions journal, July 2004

Four point function of N = 4 $$ \mathcal{N}=4 $$ stress-tensor multiplet at strong coupling journal, April 2015

Anomalous dimensions of non-chiral operators from AdS/CFT journal, October 2011

Comments on operators with large spin journal, November 2007

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

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The analytic bootstrap and AdS superhorizon locality journal, December 2013

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

Non-abelian binding energies from the lightcone bootstrap journal, February 2016

Conformal Regge theory journal, December 2012

Conformal collider physics from the lightcone bootstrap journal, February 2016

Positivity constraints for anomalous dimensions journal, October 1973

An algebraic approach to the analytic bootstrap journal, April 2017

Convexity and liberation at large spin journal, November 2013

The operator product expansion of SYM and the 4-point functions of supergravity journal, November 2000

Operator product expansion of the lowest weight CPOs in =4 at strong coupling journal, October 2000

Graviton exchange and complete four-point functions in the AdS/CFT correspondence journal, November 1999

Looking for a bulk point journal, January 2017

Bounding the space of holographic CFTs with chaos journal, October 2016

Notes on spinning operators in fermionic CFT journal, May 2017

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

A proof of the conformal collider bounds journal, June 2016

Correlation functions in the CFTd/AdSd+1 correspondence journal, April 1999

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

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

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

Universal anomalous dimensions at large spin and large twist journal, July 2015

Spinning AdS propagators journal, September 2014

Witten diagrams revisited: the AdS geometry of conformal blocks journal, January 2016

Unitarity and the holographic S-Matrix journal, October 2012

The lightcone bootstrap and the spectrum of the 3d Ising CFT journal, March 2017

Lessons from crossing symmetry at large N journal, June 2015

Generalized additivity in unitary conformal field theories journal, October 2015

Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions journal, August 2001

Correlation functions and massive Kaluza–Klein modes in the AdS/CFT correspondence journal, August 2003

Holography from conformal field theory journal, October 2009

Towards Feynman rules for Mellin amplitudes in AdS/CFT journal, October 2011

AdS/CFT four-point functions: How to succeed at z-integrals without really trying journal, November 1999

Analytic bootstrap at large spin journal, November 2015

Holography from Conformal Field Theory text, January 2009

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

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

Conformal Regge theory text, January 2012

Lessons from crossing symmetry at large N preprint, January 2014

Generalized Additivity in Unitary Conformal Field Theories text, January 2014

A bound on chaos text, January 2015

Universal anomalous dimensions at large spin and large twist text, January 2015

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks text, January 2015

Causality Constraints in Conformal Field Theory text, January 2015

Conformal Collider Physics from the Lightcone Bootstrap text, January 2015

Bounding the Space of Holographic CFTs with Chaos text, January 2016

A Proof of the Conformal Collider Bounds text, January 2016

Notes on Spinning Operators in Fermionic CFT text, January 2017

Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions text, January 2006

Correlation functions in the CFT(d)/AdS(d+1) correpondence text, January 1998

Unmixing supergravity journal, February 2018

The analytic functional bootstrap. Part II. Natural bases for the crossing equation journal, February 2019

p-adic Mellin amplitudes journal, April 2019

Recursion relations in Witten diagrams and conformal partial waves journal, May 2019

On Mellin amplitudes in SCFTs with eight supercharges journal, July 2018

On superconformal four-point Mellin amplitudes in dimension d > 2 journal, August 2018

Gravitational S-matrix from CFT dispersion relations journal, December 2018

Recursion relations in p -adic Mellin Space journal, June 2019

Loop Corrections to Supergravity on AdS 5 × S 5 journal, October 2017

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

Conformal Bootstrap in the Regge Limit text, January 2017

Quantum Gravity from Conformal Field Theory text, January 2017

Unmixing Supergravity text, January 2017

How to Succeed at Holographic Correlators Without Really Trying text, January 2017

Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE text, January 2017

Double-Trace Deformations of Conformal Correlations text, January 2018

The Conformal Bootstrap at Finite Temperature text, January 2018

On Mellin Amplitudes in SCFTs with Eight Supercharges text, January 2018

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

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text, January 2018

Anomalous Dimensions from Crossing Kernels text, January 2018

Aspects of superconformal field theories in six dimensions
journal, July 2004

Four point function of N = 4 $$ \mathcal{N}=4 $$ stress-tensor multiplet at strong coupling
journal, April 2015

Anomalous dimensions of non-chiral operators from AdS/CFT
journal, October 2011

Comments on operators with large spin
journal, November 2007

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

A bound on chaos
journal, August 2016

Causality constraints in conformal field theory
journal, May 2016

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

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

Non-abelian binding energies from the lightcone bootstrap
journal, February 2016

Conformal Regge theory
journal, December 2012

Conformal collider physics from the lightcone bootstrap
journal, February 2016

Positivity constraints for anomalous dimensions
journal, October 1973

An algebraic approach to the analytic bootstrap
journal, April 2017

Convexity and liberation at large spin
journal, November 2013

The operator product expansion of SYM and the 4-point functions of supergravity
journal, November 2000

Operator product expansion of the lowest weight CPOs in =4 at strong coupling
journal, October 2000

Graviton exchange and complete four-point functions in the AdS/CFT correspondence
journal, November 1999

Looking for a bulk point
journal, January 2017

Bounding the space of holographic CFTs with chaos
journal, October 2016

Notes on spinning operators in fermionic CFT
journal, May 2017

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

A proof of the conformal collider bounds
journal, June 2016

Correlation functions in the CFTd/AdSd+1 correspondence
journal, April 1999

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

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

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

Universal anomalous dimensions at large spin and large twist
journal, July 2015

Spinning AdS propagators
journal, September 2014

Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016

Unitarity and the holographic S-Matrix
journal, October 2012

The lightcone bootstrap and the spectrum of the 3d Ising CFT
journal, March 2017

Lessons from crossing symmetry at large N
journal, June 2015

Generalized additivity in unitary conformal field theories
journal, October 2015

Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions
journal, August 2001

Correlation functions and massive Kaluza–Klein modes in the AdS/CFT correspondence
journal, August 2003

Holography from conformal field theory
journal, October 2009

Towards Feynman rules for Mellin amplitudes in AdS/CFT
journal, October 2011

AdS/CFT four-point functions: How to succeed at z-integrals without really trying
journal, November 1999

Analytic bootstrap at large spin
journal, November 2015

Holography from Conformal Field Theory
text, January 2009

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

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

Conformal Regge theory
text, January 2012

Lessons from crossing symmetry at large N
preprint, January 2014

Generalized Additivity in Unitary Conformal Field Theories
text, January 2014

A bound on chaos
text, January 2015

Universal anomalous dimensions at large spin and large twist
text, January 2015

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
text, January 2015

Causality Constraints in Conformal Field Theory
text, January 2015

Conformal Collider Physics from the Lightcone Bootstrap
text, January 2015

Bounding the Space of Holographic CFTs with Chaos
text, January 2016

A Proof of the Conformal Collider Bounds
text, January 2016

Notes on Spinning Operators in Fermionic CFT
text, January 2017

Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
text, January 2006

Correlation functions in the CFT(d)/AdS(d+1) correpondence
text, January 1998

Unmixing supergravity
journal, February 2018

The analytic functional bootstrap. Part II. Natural bases for the crossing equation
journal, February 2019

p-adic Mellin amplitudes
journal, April 2019

Recursion relations in Witten diagrams and conformal partial waves
journal, May 2019

On Mellin amplitudes in SCFTs with eight supercharges
journal, July 2018

On superconformal four-point Mellin amplitudes in dimension d > 2
journal, August 2018

Gravitational S-matrix from CFT dispersion relations
journal, December 2018

Recursion relations in p -adic Mellin Space
journal, June 2019

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

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

Conformal Bootstrap in the Regge Limit
text, January 2017

Quantum Gravity from Conformal Field Theory
text, January 2017

Unmixing Supergravity
text, January 2017

How to Succeed at Holographic Correlators Without Really Trying
text, January 2017

Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
text, January 2017

Double-Trace Deformations of Conformal Correlations
text, January 2018

The Conformal Bootstrap at Finite Temperature
text, January 2018

On Mellin Amplitudes in SCFTs with Eight Supercharges
text, January 2018

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

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
text, January 2018

Anomalous Dimensions from Crossing Kernels
text, January 2018

Polyakov-Mellin Bootstrap for AdS loops
text, January 2018

Recursion Relations in Witten Diagrams and Conformal Partial Waves
text, January 2018