An algebraic approach to the analytic bootstrap

Alday, Luis F.; Zhiboedov, Alexander

doi:10.1007/JHEP04(2017)157

Title: An algebraic approach to the analytic bootstrap

Abstract

We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. Here, we analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O(N ) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O(N ) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents.

Authors:

Alday, Luis F. ^[1]; Zhiboedov, Alexander ^[2]

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

Publication Date:: Thu Apr 27 00:00:00 EDT 2017

Research Org.:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); European Research Council (ERC)

OSTI Identifier:: 1368372

Grant/Contract Number:: SC0007870; 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: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal Field Theory; AdS-CFT Correspondence

Citation Formats


                    Alday, Luis F., and Zhiboedov, Alexander. An algebraic approach to the analytic bootstrap.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP04(2017)157.

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                    Alday, Luis F., & Zhiboedov, Alexander. An algebraic approach to the analytic bootstrap.  United States.  https://doi.org/10.1007/JHEP04(2017)157

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                    Alday, Luis F., and Zhiboedov, Alexander. Thu .  
"An algebraic approach to the analytic bootstrap".  United States.  https://doi.org/10.1007/JHEP04(2017)157.  https://www.osti.gov/servlets/purl/1368372.

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@article{osti_1368372,

  title        = {An algebraic approach to the analytic bootstrap},

  author       = {Alday, Luis F. and Zhiboedov, Alexander},

  abstractNote = {We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. Here, we analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O(N ) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O(N ) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents.},

  doi          = {10.1007/JHEP04(2017)157},

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

  number       = 4,

  volume       = 2017,

  place        = {United States},

  year         = {Thu Apr 27 00:00:00 EDT 2017},

  month        = {Thu Apr 27 00:00:00 EDT 2017}

}

Copy to clipboard

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Title: An algebraic approach to the analytic bootstrap

Abstract

Citation Formats

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

Evolution equations beyond one loop from conformal symmetry journal, August 2013

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

Comments on operators with large spin journal, November 2007

Bootstrapping the O(N) archipelago journal, November 2015

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

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

Causality constraints in conformal field theory journal, May 2016

The analytic bootstrap and AdS superhorizon locality journal, December 2013

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

A simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion journal, June 1998

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

CT and CJ up to next-to-leading order in in the conformally invariant O(N) vector model for 2 < d < 4 journal, October 1995

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

Higher-spin correlators journal, October 2013

Convexity and liberation at large spin journal, November 2013

Conformal four point functions and the operator product expansion journal, April 2001

Anomalous dimensions of high-spin operators beyond the leading order journal, July 2007

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents journal, June 2014

Critical phenomena and renormalization-group theory journal, October 2002

Analytic bootstrap at large spin journal, November 2015

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion text, January 1973

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

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

Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents text, January 2014

Lessons from crossing symmetry at large N preprint, January 2014

Eikonalization of Conformal Blocks text, January 2015

Causality Constraints in Conformal Field Theory text, January 2015

The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion text, January 1997

Inverse bootstrapping conformal field theories journal, January 2018

General bootstrap equations in 4D CFTs journal, January 2018

Quantum Regge trajectories and the Virasoro analytic bootstrap journal, May 2019

Scalar-fermion analytic bootstrap in 4D journal, June 2019

Loops in AdS from conformal field theory journal, July 2017

Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory journal, July 2018

Holographic reconstruction of AdS exchanges from crossing symmetry journal, August 2017

Solving CFTs with weakly broken higher spin symmetry journal, October 2017

Analytic Euclidean bootstrap journal, October 2019

Conformal bootstrap in the Regge limit journal, December 2017

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Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics text, January 2017

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text, January 2017

Universality at large transverse spin in defect CFT text, January 2018

Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics text, January 2017

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Solving CFTs with Weakly Broken Higher Spin Symmetry text, January 2016

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

Conformal Bootstrap in the Regge Limit text, January 2017

Weight Shifting Operators and Conformal Blocks text, January 2017

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text, January 2017

Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory text, January 2017

Scalar CFTs and Their Large N Limits text, January 2017

Scalar-Fermion Analytic Bootstrap in 4D preprint, January 2017

Double-Trace Deformations of Conformal Correlations text, January 2018

The Conformal Bootstrap at Finite Temperature text, January 2018

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

Anomalous Dimensions from Crossing Kernels text, January 2018

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

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journal, August 2013

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

Comments on operators with large spin
journal, November 2007

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journal, June 2016

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journal, June 1998

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

CT and CJ up to next-to-leading order in in the conformally invariant O(N) vector model for 2 < d < 4
journal, October 1995

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

Higher-spin correlators
journal, October 2013

Convexity and liberation at large spin
journal, November 2013

Conformal four point functions and the operator product expansion
journal, April 2001

Anomalous dimensions of high-spin operators beyond the leading order
journal, July 2007

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014

Critical phenomena and renormalization-group theory
journal, October 2002

Analytic bootstrap at large spin
journal, November 2015

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion
text, January 1973

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

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

Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
text, January 2014

Lessons from crossing symmetry at large N
preprint, January 2014

Eikonalization of Conformal Blocks
text, January 2015

Causality Constraints in Conformal Field Theory
text, January 2015

The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion
text, January 1997

Inverse bootstrapping conformal field theories
journal, January 2018

General bootstrap equations in 4D CFTs
journal, January 2018

Quantum Regge trajectories and the Virasoro analytic bootstrap
journal, May 2019

Scalar-fermion analytic bootstrap in 4D
journal, June 2019

Loops in AdS from conformal field theory
journal, July 2017

Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
journal, July 2018

Holographic reconstruction of AdS exchanges from crossing symmetry
journal, August 2017

Solving CFTs with weakly broken higher spin symmetry
journal, October 2017

Analytic Euclidean bootstrap
journal, October 2019

Conformal bootstrap in the Regge limit
journal, December 2017

Critical O( N ) model to order ϵ ⁴ from analytic bootstrap
journal, December 2018

Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics
text, January 2017

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
text, January 2017

Universality at large transverse spin in defect CFT
text, January 2018

Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics
text, January 2017

Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
text, January 2018

Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics
text, January 2017

Solving CFTs with Weakly Broken Higher Spin Symmetry
text, January 2016

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

Conformal Bootstrap in the Regge Limit
text, January 2017

Weight Shifting Operators and Conformal Blocks
text, January 2017

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
text, January 2017

Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
text, January 2017

Scalar CFTs and Their Large N Limits
text, January 2017

Scalar-Fermion Analytic Bootstrap in 4D
preprint, January 2017

Double-Trace Deformations of Conformal Correlations
text, January 2018

The Conformal Bootstrap at Finite Temperature
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

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

A Study of Quantum Field Theories in AdS at Finite Coupling
text, January 2018

Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
text, January 2018

A Crossing-Symmetric OPE Inversion Formula
text, January 2018

An Analytic Approach to BCFT$_d$
text, January 2018

Closed-form expression for cross-channel conformal blocks near the lightcone
text, January 2019

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$
text, January 2019