Bootstrapping mixed correlators in the 3D Ising model

Kos, Filip; Poland, David; Simmons-Duffin, David

doi:10.1007/JHEP11(2014)109

Title: Bootstrapping mixed correlators in the 3D Ising model

Abstract

We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a Z₂ global symmetry. For the leading Z₂-odd operator σ and Z₂-even operator ϵ, we obtain numerical constraints on the allowed dimensions (Δ _σ , Δ _ϵ ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ _σ , Δ _ϵ ) space compatible with the known values in the 3D Ising CFT.

Authors:

Kos, Filip ^[1]; Poland, David ^[1]; Simmons-Duffin, David ^[2]

Yale Univ., New Haven, CT (United States). Department of Physics
Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

Publication Date:: Thu Nov 20 00:00:00 EST 2014

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1454736

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: 2014; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Nonperturbative Effects; Discrete and Finite Symmetries

Citation Formats


                    Kos, Filip, Poland, David, and Simmons-Duffin, David. Bootstrapping mixed correlators in the 3D Ising model.  United States: N. p., 2014. 
Web.  doi:10.1007/JHEP11(2014)109.

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                    Kos, Filip, Poland, David, & Simmons-Duffin, David. Bootstrapping mixed correlators in the 3D Ising model.  United States.  https://doi.org/10.1007/JHEP11(2014)109

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                    Kos, Filip, Poland, David, and Simmons-Duffin, David. Thu .  
"Bootstrapping mixed correlators in the 3D Ising model".  United States.  https://doi.org/10.1007/JHEP11(2014)109.  https://www.osti.gov/servlets/purl/1454736.

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@article{osti_1454736,

  title        = {Bootstrapping mixed correlators in the 3D Ising model},

  author       = {Kos, Filip and Poland, David and Simmons-Duffin, David},

  abstractNote = {We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a Z2 global symmetry. For the leading Z2-odd operator σ and Z2-even operator ϵ, we obtain numerical constraints on the allowed dimensions (Δ σ , Δ ϵ ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ σ , Δ ϵ ) space compatible with the known values in the 3D Ising CFT.},

  doi          = {10.1007/JHEP11(2014)109},

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

  number       = 11,

  volume       = 2014,

  place        = {United States},

  year         = {Thu Nov 20 00:00:00 EST 2014},

  month        = {Thu Nov 20 00:00:00 EST 2014}

}

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Necessary Condition for Emergent Symmetry from the Conformal Bootstrap
journal, September 2016

Nakayama, Yu; Ohtsuki, Tomoki
Physical Review Letters, Vol. 117, Issue 13
DOI: 10.1103/PhysRevLett.117.131601

Long multiplet bootstrap
text, January 2017

Cornagliotto, Martina; Lemos, Madalena; Schomerus, Volker
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-11762

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

Isachenkov, Mikhail; Schomerus, Volker
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-03900

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

Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-11690

Conformal perturbation theory confronts lattice results in the vicinity of a critical point
text, January 2019

Caselle, Michele; Magnoli, Nicodemo; Nada, Alessandro
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-03032

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

Kaviraj, Apratim; Sen, Kallol; Sinha, Aninda
arXiv
DOI: 10.48550/arxiv.1504.00772

Bootstrapping 3D Fermions
text, January 2015

Iliesiu, Luca; Kos, Filip; Poland, David
arXiv
DOI: 10.48550/arxiv.1508.00012

Causality Constraints in Conformal Field Theory
text, January 2015

Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
arXiv
DOI: 10.48550/arxiv.1509.00014

Precision Islands in the Ising and $O(N)$ Models
text, January 2016

Kos, Filip; Poland, David; Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1603.04436

The Effective Bootstrap
preprint, January 2016

Echeverri, Alejandro Castedo; von Harling, Benedict; Serone, Marco
arXiv
DOI: 10.48550/arxiv.1606.02771

Analyticity in Spin in Conformal Theories
text, January 2017

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

Bootstrap experiments on higher dimensional CFTs
text, January 2017

Nakayama, Yu
arXiv
DOI: 10.48550/arxiv.1705.02744

Bootstrapping 3D Fermions with Global Symmetries
text, January 2017

Iliesiu, Luca; Kos, Filip; Poland, David
arXiv
DOI: 10.48550/arxiv.1705.03484

Weight Shifting Operators and Conformal Blocks
text, January 2017

Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1706.07813

The 3d Stress-Tensor Bootstrap
text, January 2017

Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr
arXiv
DOI: 10.48550/arxiv.1708.05718

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

Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
arXiv
DOI: 10.48550/arxiv.1711.00016

The Analytic Bootstrap in Fermionic CFTs
text, January 2017

van Loon, Mark
arXiv
DOI: 10.48550/arxiv.1711.02099

Anomalous dimensions of spinning operators from conformal symmetry
text, January 2017

Gliozzi, Ferdinando
arXiv
DOI: 10.48550/arxiv.1711.05530

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

Isachenkov, Mikhail; Schomerus, Volker
arXiv
DOI: 10.48550/arxiv.1711.06609

Solving M-theory with the Conformal Bootstrap
text, January 2017

Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
arXiv
DOI: 10.48550/arxiv.1711.07343

Scalar CFTs and Their Large N Limits
text, January 2017

Rong, Junchen; Su, Ning
arXiv
DOI: 10.48550/arxiv.1712.00985

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

Poland, David; Rychkov, Slava; Vichi, Alessandro
arXiv
DOI: 10.48550/arxiv.1805.04405

Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
text, January 2018

Kousvos, Stefanos R.; Stergiou, Andreas
arXiv
DOI: 10.48550/arxiv.1810.10015

The S-matrix Bootstrap IV: Multiple Amplitudes
text, January 2019

Homrich, Alexandre; Penedones, Joao; Toledo, Jonathan
arXiv
DOI: 10.48550/arxiv.1905.06905

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

Li, Wenliang
arXiv
DOI: 10.48550/arxiv.1906.00707

Convergence of Non-Perturbative Approximations to the Renormalization Group
text, January 2019

Balog, Ivan; Chaté, Hugues; Delamotte, Bertrand
arXiv
DOI: 10.48550/arxiv.1907.01829

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Title: Bootstrapping mixed correlators in the 3D Ising model

Abstract

Citation Formats

Carving out the space of 4D CFTs journal, May 2012

Mellin amplitudes for dual conformal integrals journal, August 2012

Finite size scaling study of lattice models in the three-dimensional Ising universality class journal, November 2010

A note on CFT correlators in three dimensions journal, July 2013

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

N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators journal, August 2014

The analytic bootstrap and AdS superhorizon locality journal, December 2013

Spinning conformal blocks journal, November 2011

Conformal Regge theory journal, December 2012

Constraints on Conformal Field Theories in Diverse Dimensions from the Bootstrap Mechanism journal, October 2013

Analyticity properties and asymptotic expansions of conformal covariant Green's functions journal, February 1974

Bootstrapping the 3d Ising twist defect journal, March 2014

Generalized S -procedure and finite frequency KYP lemma journal, January 2000

Spinning conformal correlators journal, November 2011

The bootstrap program for boundary CFT d journal, July 2013

Conformal blocks for highly disparate scaling dimensions journal, September 2014

Manifestly conformal covariant operator-product expansion journal, December 1971

Scaling, universality, and renormalization: Three pillars of modern critical phenomena journal, March 1999

Critical exponents by the scaling-field method: The isotropic N -vector model in three dimensions journal, December 1984

Critical exponents of the 3d Ising and related models from conformal bootstrap journal, October 2014

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

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

Superconformal symmetry, correlation functions and the operator product expansion journal, May 2002

Conformal blocks for arbitrary spins in two dimensions journal, November 2012

Superconformal Ward identities and their solution journal, April 2005

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

Universality of long-distance AdS physics from the CFT bootstrap journal, August 2014

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

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

Bounds on 4D conformal and superconformal field theories journal, May 2011

Covariant expansion of the conformal four -point function journal, December 1972

Convexity and liberation at large spin journal, November 2013

Conformal blocks in the large D limit journal, August 2013

Critical phenomena and renormalization-group theory journal, October 2002

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

N = 4 Superconformal Bootstrap journal, August 2013

Bootstrapping Conformal Field Theories with the Extremal Functional Method journal, December 2013

On Four-Point Functions of Half-BPS Operators in General Dimensions journal, September 2004

Problems and Theorems in Analysis book, January 1976

Subleading critical exponents from the renormalisation group journal, February 2004

Conformal Field Theories in Fractional Dimensions journal, April 2014

Unitarity and the holographic S-Matrix journal, October 2012

Bounds on N $$ \mathcal{N} $$ = 1 superconformal theories with global symmetries journal, August 2014

Covariant approaches to superconformal blocks journal, August 2014

Projectors, shadows, and conformal blocks journal, April 2014

Bounds on OPE coefficients in 4D Conformal Field Theories journal, October 2014

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

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

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

Towards Haskell in the cloud journal, January 2012

Current OPEs in superconformal theories journal, September 2011

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

Problems and Theorems in Analysis book, January 1972

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

Properties of Partial-Wave Amplitudes in Conformal Invariant Field Theories text, January 1975

Holography from Conformal Field Theory text, January 2009

More Holography from Conformal Field Theory text, January 2010

A Note on CFT Correlators in Three Dimensions preprint, January 2011

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

Current OPEs in Superconformal Theories text, January 2011

Spinning Conformal Blocks text, January 2011

Analyticity and the Holographic S-Matrix text, January 2011

Mellin Amplitudes for Dual Conformal Integrals text, January 2012

Conformal Blocks for Arbitrary Spins in Two Dimensions text, January 2012

Conformal Regge theory text, January 2012

The Bootstrap Program for Boundary CFT_d text, January 2012

Bootstrapping Conformal Field Theories with the Extremal Functional Method text, January 2012

Conformal Blocks in the Large D Limit text, January 2013

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

Conformal Field Theories in Fractional Dimensions text, January 2013

Bootstrapping the 3d Ising twist defect text, January 2013

Covariant Approaches to Superconformal Blocks text, January 2014

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

Universality of Long-Distance AdS Physics from the CFT Bootstrap text, January 2014

Carving out the space of 4D CFTs
journal, May 2012

Mellin amplitudes for dual conformal integrals
journal, August 2012

Finite size scaling study of lattice models in the three-dimensional Ising universality class
journal, November 2010

A note on CFT correlators in three dimensions
journal, July 2013

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

N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators
journal, August 2014

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Spinning conformal blocks
journal, November 2011

Conformal Regge theory
journal, December 2012

Constraints on Conformal Field Theories in Diverse Dimensions from the Bootstrap Mechanism
journal, October 2013

Analyticity properties and asymptotic expansions of conformal covariant Green's functions
journal, February 1974

Bootstrapping the 3d Ising twist defect
journal, March 2014

Generalized $S$ -procedure and finite frequency KYP lemma
journal, January 2000

Spinning conformal correlators
journal, November 2011

The bootstrap program for boundary CFT d
journal, July 2013

Conformal blocks for highly disparate scaling dimensions
journal, September 2014

Manifestly conformal covariant operator-product expansion
journal, December 1971

Scaling, universality, and renormalization: Three pillars of modern critical phenomena
journal, March 1999

Critical exponents by the scaling-field method: The isotropic $N$ -vector model in three dimensions
journal, December 1984

Critical exponents of the 3d Ising and related models from conformal bootstrap
journal, October 2014

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

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

Superconformal symmetry, correlation functions and the operator product expansion
journal, May 2002

Conformal blocks for arbitrary spins in two dimensions
journal, November 2012

Superconformal Ward identities and their solution
journal, April 2005

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

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

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

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

Bounds on 4D conformal and superconformal field theories
journal, May 2011

Covariant expansion of the conformal four -point function
journal, December 1972

Convexity and liberation at large spin
journal, November 2013

Conformal blocks in the large D limit
journal, August 2013

Critical phenomena and renormalization-group theory
journal, October 2002

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

$N = 4$ Superconformal Bootstrap
journal, August 2013

Bootstrapping Conformal Field Theories with the Extremal Functional Method
journal, December 2013

On Four-Point Functions of Half-BPS Operators in General Dimensions
journal, September 2004

Problems and Theorems in Analysis
book, January 1976

Subleading critical exponents from the renormalisation group
journal, February 2004

Conformal Field Theories in Fractional Dimensions
journal, April 2014

Unitarity and the holographic S-Matrix
journal, October 2012

Bounds on N $$ \mathcal{N} $$ = 1 superconformal theories with global symmetries
journal, August 2014

Covariant approaches to superconformal blocks
journal, August 2014

Projectors, shadows, and conformal blocks
journal, April 2014

Bounds on OPE coefficients in 4D Conformal Field Theories
journal, October 2014

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

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

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

Towards Haskell in the cloud
journal, January 2012

Current OPEs in superconformal theories
journal, September 2011

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

Problems and Theorems in Analysis
book, January 1972

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

Properties of Partial-Wave Amplitudes in Conformal Invariant Field Theories
text, January 1975

Holography from Conformal Field Theory
text, January 2009

More Holography from Conformal Field Theory
text, January 2010

A Note on CFT Correlators in Three Dimensions
preprint, January 2011

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

Current OPEs in Superconformal Theories
text, January 2011

Spinning Conformal Blocks
text, January 2011

Analyticity and the Holographic S-Matrix
text, January 2011

Mellin Amplitudes for Dual Conformal Integrals
text, January 2012

Conformal Blocks for Arbitrary Spins in Two Dimensions
text, January 2012

Conformal Regge theory
text, January 2012

The Bootstrap Program for Boundary CFT_d
text, January 2012

Bootstrapping Conformal Field Theories with the Extremal Functional Method
text, January 2012

Conformal Blocks in the Large D Limit
text, January 2013

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

Conformal Field Theories in Fractional Dimensions
text, January 2013

Bootstrapping the 3d Ising twist defect
text, January 2013

Covariant Approaches to Superconformal Blocks
text, January 2014

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

Universality of Long-Distance AdS Physics from the CFT Bootstrap
text, January 2014

Bounds on OPE Coefficients in 4D Conformal Field Theories
text, January 2014

On Four-Point Functions of Half-BPS Operators in General Dimensions
text, January 2004

Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
text, January 2004