Bootstrapping the O(N ) vector models

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

doi:10.1007/jhep06(2014)091

Title: Bootstrapping the O(N ) vector models

Abstract

We study the conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N) singlet and symmetric tensor operators appearing in the $$\phi_i \times \phi_j$$ OPE, where $$\phi_i$$ is a fundamental of O(N). Comparing these bounds to previous determinations of critical exponents in the O(N) vector models, we find strong numerical evidence that the O(N) vector models saturate the bootstrap constraints at all values of N. We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N.

Authors:

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

Yale Univ., New Haven, CT (United States)
Inst. for Advanced Study, Princeton, NJ (United States)

Publication Date:: Mon Jun 16 00:00:00 EDT 2014

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

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1599107

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: 6; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Kos, Filip, Poland, David, and Simmons-Duffin, David. Bootstrapping the O(N ) vector models.  United States: N. p., 2014. 
Web.  doi:10.1007/jhep06(2014)091.

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                    Kos, Filip, Poland, David, & Simmons-Duffin, David. Bootstrapping the O(N ) vector models.  United States.  https://doi.org/10.1007/jhep06(2014)091

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                    Kos, Filip, Poland, David, and Simmons-Duffin, David. Mon .  
"Bootstrapping the O(N ) vector models".  United States.  https://doi.org/10.1007/jhep06(2014)091.  https://www.osti.gov/servlets/purl/1599107.

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@article{osti_1599107,

  title        = {Bootstrapping the O(N ) vector models},

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

  abstractNote = {We study the conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N) singlet and symmetric tensor operators appearing in the $\phi_i \times \phi_j$ OPE, where $\phi_i$ is a fundamental of O(N). Comparing these bounds to previous determinations of critical exponents in the O(N) vector models, we find strong numerical evidence that the O(N) vector models saturate the bootstrap constraints at all values of N. We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N.},

  doi          = {10.1007/jhep06(2014)091},

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

  number       = 6,

  volume       = 2014,

  place        = {United States},

  year         = {Mon Jun 16 00:00:00 EDT 2014},

  month        = {Mon Jun 16 00:00:00 EDT 2014}

}

Copy to clipboard

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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 the long-range Ising model in three dimensions
text, January 2018

Behan, Connor
arXiv
DOI: 10.48550/arxiv.1810.07199

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

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

2d small N=4 Long-multiplet superconformal block
text, January 2018

Kos, Filip; Oh, Jihwan
arXiv
DOI: 10.48550/arxiv.1810.10029

Large $N_f$ quantum field theory
text, January 2018

Gracey, J. A.
arXiv
DOI: 10.48550/arxiv.1812.05368

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

Li, Wenliang
arXiv
DOI: 10.48550/arxiv.1906.00707

Fusion of spin fields in $W_3$ conformal field theories
text, January 2019

Ikhlef, Yacine; Shimada, Hirohiko
arXiv
DOI: 10.48550/arxiv.1906.01323

Conformal invariance and vector operators in the $O(N)$ model
text, January 2019

De Polsi, Gonzalo; Tissier, Matthieu; Wschebor, Nicolás
arXiv
DOI: 10.48550/arxiv.1907.09981

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Title: Bootstrapping the O(N ) vector models

Abstract

Citation Formats

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

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

The analytic bootstrap and AdS superhorizon locality journal, December 2013

Feynman-Graph Expansion for the Equation of State near the Critical Point journal, January 1973

Constraining conformal field theories with a slightly broken higher spin symmetry journal, May 2013

Spinning conformal correlators journal, November 2011

The bootstrap program for boundary CFT d journal, July 2013

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice journal, June 2002

Massless mixed-symmetry bosonic free fields in d-dimensional anti-de Sitter space-time journal, July 1995

All unitary ray representations of the conformal group SU(2,2) with positive energy text, January 1975

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

Critical exponents and equation of state of the three-dimensional Heisenberg universality class journal, April 2002

AdS dual of the critical O(N) vector model journal, December 2002

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

Harmonic crossover exponents in O ( n ) models with the pseudo- ϵ expansion approach journal, February 2005

Convexity and liberation at large spin journal, November 2013

Critical phenomena and renormalization-group theory journal, October 2002

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

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model journal, July 1996

All unitary ray representations of the conformal group SU(2,2) with positive energy journal, February 1977

Unitarity and the holographic S-Matrix journal, October 2012

Projectors, shadows, and conformal blocks journal, April 2014

Theoretical estimates of the critical exponents of the superfluid transition in He 4 by lattice methods journal, October 2006

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

Comments on unparticles journal, May 2008

Mellin amplitudes for dual conformal integrals journal, August 2012

Spinning conformal blocks journal, November 2011

Crossover exponent in O ( N ) φ 4 theory at O ( 1 / N 2 ) journal, August 2002

Quantum field theory in the large N limit: a review journal, October 2003

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

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

Conformal blocks in the large D limit journal, August 2013

Restrictions imposed by superconformal invariance on quantum field theories journal, January 1998

N = 4 Superconformal Bootstrap journal, August 2013

The scalar ancestor of the energy-momentum field in critical σ-models at 2 < d < 4 journal, January 1992

The critical equation of state of the three-dimensional universality class: journal, January 2005

Semidefinite Programming journal, March 1996

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

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

The renormalization group and the ε expansion journal, August 1974

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

Critical exponents and equation of state of the three-dimensional Heisenberg universality class text, January 2002

Comments on Unparticles text, January 2008

Bounds on 4D Conformal and Superconformal Field Theories text, January 2010

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

Spinning Conformal Blocks text, January 2011

Analyticity and the Holographic S-Matrix text, January 2011

Projectors, Shadows, and Conformal Blocks text, January 2012

The Bootstrap Program for Boundary CFT_d text, January 2012

Conformal Blocks in the Large D Limit text, January 2013

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice text, January 2002

Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model text, January 1994

Restrictions Imposed by Superconformal Invariance on Quantum Field Theories text, January 1997

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model journal, July 1996

Constraining conformal field theories with a slightly broken higher spin symmetry journal, May 2013

Harmonic Analysis on Homogeneous Spaces book, January 1973

Rigorous limits on the interaction strength in quantum field theory journal, April 2010

Universal Constraints on Conformal Operator Dimensions text, January 2009

Spinning Conformal Correlators text, January 2011

Constraining conformal field theories with a higher spin symmetry preprint, January 2011

Mellin Amplitudes for Dual Conformal Integrals text, January 2012

Radial Coordinates for Conformal Blocks text, January 2013

Critical exponents and equation of state of the three-dimensional Heisenberg universality class text, January 2001

Crossover exponent in O(N) phi^4 theory at O(1/N^2) text, January 2002

Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach text, January 2004

The critical exponents of the superfluid transition in He4 text, January 2006

Restrictions Imposed by Superconformal Invariance on Quantum Field Theories text, January 1997

Conformal Invariance and Vector Operators in the O(N) Model journal, October 2019

Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations journal, April 2017

The conformal bootstrap journal, June 2016

Inverse bootstrapping conformal field theories journal, January 2018

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

Eikonalization of conformal blocks journal, September 2015

Bootstrapping O ( N ) vector models in 4 < d < 6 journal, April 2015

Bound states of the ϕ 4 model via the nonperturbative renormalization group journal, June 2016

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

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

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Feynman-Graph Expansion for the Equation of State near the Critical Point
journal, January 1973

Constraining conformal field theories with a slightly broken higher spin symmetry
journal, May 2013

Spinning conformal correlators
journal, November 2011

The bootstrap program for boundary CFT d
journal, July 2013

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice
journal, June 2002

Massless mixed-symmetry bosonic free fields in d-dimensional anti-de Sitter space-time
journal, July 1995

All unitary ray representations of the conformal group SU(2,2) with positive energy
text, January 1975

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

Critical exponents and equation of state of the three-dimensional Heisenberg universality class
journal, April 2002

AdS dual of the critical O(N) vector model
journal, December 2002

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

Harmonic crossover exponents in $O (n)$ models with the pseudo- $ϵ$ expansion approach
journal, February 2005

Convexity and liberation at large spin
journal, November 2013

Critical phenomena and renormalization-group theory
journal, October 2002

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

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model
journal, July 1996

All unitary ray representations of the conformal group SU(2,2) with positive energy
journal, February 1977

Unitarity and the holographic S-Matrix
journal, October 2012

Projectors, shadows, and conformal blocks
journal, April 2014

Theoretical estimates of the critical exponents of the superfluid transition in ${}^{4}{He}$ by lattice methods
journal, October 2006

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

Comments on unparticles
journal, May 2008

Mellin amplitudes for dual conformal integrals
journal, August 2012

Spinning conformal blocks
journal, November 2011

Crossover exponent in $O (N)$ $φ^{4}$ theory at ${O (1 / N}^{2})$
journal, August 2002

Quantum field theory in the large N limit: a review
journal, October 2003

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

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

Conformal blocks in the large D limit
journal, August 2013

Restrictions imposed by superconformal invariance on quantum field theories
journal, January 1998

$N = 4$ Superconformal Bootstrap
journal, August 2013

The scalar ancestor of the energy-momentum field in critical σ-models at 2 < d < 4
journal, January 1992

The critical equation of state of the three-dimensional universality class:
journal, January 2005

Semidefinite Programming
journal, March 1996

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

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

The renormalization group and the ε expansion
journal, August 1974

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

Critical exponents and equation of state of the three-dimensional Heisenberg universality class
text, January 2002

Comments on Unparticles
text, January 2008

Bounds on 4D Conformal and Superconformal Field Theories
text, January 2010

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

Spinning Conformal Blocks
text, January 2011

Analyticity and the Holographic S-Matrix
text, January 2011

Projectors, Shadows, and Conformal Blocks
text, January 2012

The Bootstrap Program for Boundary CFT_d
text, January 2012

Conformal Blocks in the Large D Limit
text, January 2013

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
text, January 2002

Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
text, January 1994

Restrictions Imposed by Superconformal Invariance on Quantum Field Theories
text, January 1997

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model
journal, July 1996

Constraining conformal field theories with a slightly broken higher spin symmetry
journal, May 2013

Harmonic Analysis on Homogeneous Spaces
book, January 1973

Rigorous limits on the interaction strength in quantum field theory
journal, April 2010

Universal Constraints on Conformal Operator Dimensions
text, January 2009

Spinning Conformal Correlators
text, January 2011

Constraining conformal field theories with a higher spin symmetry
preprint, January 2011

Mellin Amplitudes for Dual Conformal Integrals
text, January 2012

Radial Coordinates for Conformal Blocks
text, January 2013

Critical exponents and equation of state of the three-dimensional Heisenberg universality class
text, January 2001

Crossover exponent in O(N) phi^4 theory at O(1/N^2)
text, January 2002

Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
text, January 2004

The critical exponents of the superfluid transition in He4
text, January 2006

Restrictions Imposed by Superconformal Invariance on Quantum Field Theories
text, January 1997

Conformal Invariance and Vector Operators in the O(N) Model
journal, October 2019

Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations
journal, April 2017

The conformal bootstrap
journal, June 2016

Inverse bootstrapping conformal field theories
journal, January 2018

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

Eikonalization of conformal blocks
journal, September 2015

Bootstrapping $O (N)$ vector models in $4 < d < 6$
journal, April 2015

Bound states of the $ϕ^{4}$ model via the nonperturbative renormalization group
journal, June 2016

Fermion conformal bootstrap in 4d
journal, June 2019

Fractal Dimensions of Self-Avoiding Walks and Ising High-Temperature Graphs in 3D Conformal Bootstrap
journal, November 2016

2d small N=4 Long-multiplet superconformal block
journal, February 2019