Universal bounds on operator dimensions from the average null energy condition

Córdova, Clay; Diab, Kenan

doi:10.1007/jhep02(2018)131

Title: Universal bounds on operator dimensions from the average null energy condition

Abstract

We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional conformal field theories. Denoting the spin of an operator by a pair of integers ($$k\overline{k}\ $$) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin ($$k\overline{k}\ $$) and scaling dimension Δ satisfy Δ ≥ max{$$k\overline{k}\ $$}. If |$$k-\overline{k}\ $$| > 4 , this is stronger than the unitarity bound.

Authors:

Córdova, Clay ^[1];

^[2]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Princeton Univ., NJ (United States). Dept. of Physics

Publication Date:: Wed Feb 21 00:00:00 EST 2018

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

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

OSTI Identifier:: 1502475

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: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Higher Spin Symmetry

Citation Formats


                    Córdova, Clay, and Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep02(2018)131.

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                    Córdova, Clay, & Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition.  United States.  https://doi.org/10.1007/jhep02(2018)131

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                    Córdova, Clay, and Diab, Kenan. Wed .  
"Universal bounds on operator dimensions from the average null energy condition".  United States.  https://doi.org/10.1007/jhep02(2018)131.  https://www.osti.gov/servlets/purl/1502475.

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@article{osti_1502475,

  title        = {Universal bounds on operator dimensions from the average null energy condition},

  author       = {Córdova, Clay and Diab, Kenan},

  abstractNote = {We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional conformal field theories. Denoting the spin of an operator by a pair of integers ($k\overline{k}\ $) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin ($k\overline{k}\ $) and scaling dimension Δ satisfy Δ ≥ max{$k\overline{k}\ $}. If |$k-\overline{k}\ $| > 4 , this is stronger than the unitarity bound.},

  doi          = {10.1007/jhep02(2018)131},

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

  number       = 2,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Feb 21 00:00:00 EST 2018},

  month        = {Wed Feb 21 00:00:00 EST 2018}

}

Copy to clipboard

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https://doi.org/10.1007/jhep02(2018)131

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Cited by: 20 works

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Table 1: Null states of primary operators saturating a unitarity bound.

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Implications of ANEC for SCFTs in four dimensions
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Title: Universal bounds on operator dimensions from the average null energy condition

Abstract

Citation Formats

Figures / Tables:

Topological censorship journal, September 1993

Constraints on parity violating conformal field theories in d = 3 journal, November 2017

Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions journal, March 2016

On superconformal characters and partition functions in three dimensions journal, February 2010

Limits on massless particles journal, October 1980

Aspects of superconformal multiplets in D > 4 journal, November 2016

Averaged null energy condition from causality journal, July 2017

Higher derivative gravity, causality and positivity of energy in a UV complete QFT journal, December 2009

AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound journal, March 2010

Spectral sum rules for conformal field theories in arbitrary dimensions journal, July 2017

Spinning conformal correlators journal, November 2011

Nonpositivity of the energy density in quantized field theories journal, April 1965

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

General bootstrap equations in 4D CFTs journal, January 2018

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition journal, September 2016

Implications of Conformal Invariance in Field Theories for General Dimensions journal, May 1994

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

On conformal field theories with extremal $ \frac{a}{c} $ values journal, April 2014

Counting conformal correlators journal, February 2018

Two-point functions of conformal primary operators in N $$ \mathcal{N} $$ = 1 superconformal theories journal, October 2014

Conformal collider physics: energy and charge correlations journal, May 2008

On short and semi-short representations for four-dimensional superconformal symmetry journal, September 2003

Holographic GB gravity in arbitrary dimensions journal, March 2010

General three-point functions in 4D CFT journal, January 2015

Bounds on OPE coefficients from interference effects in the conformal collider journal, November 2017

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

On Superconformal Characters and Partition Functions in Three Dimensions text, January 2008

Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT text, January 2009

AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound text, January 2009

Holographic GB gravity in arbitrary dimensions text, January 2009

Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions text, January 2015

A Proof of the Conformal Collider Bounds text, January 2016

Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition text, January 2016

Spectral sum rules for conformal field theories in arbitrary dimensions text, January 2016

Counting Conformal Correlators preprint, January 2016

On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry text, January 2002

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

Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren journal, February 1977

A proof of the conformal collider bounds journal, June 2016

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

On Conformal Field Theories With Extremal a/c Values text, January 2013

Implications of ANEC for SCFTs in four dimensions journal, January 2020

Exploring 2-group global symmetries journal, February 2019

Higher spin ANEC and the space of CFTs journal, July 2019

Correlators of mixed symmetry operators in defect CFTs journal, October 2018

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

The conformal bootstrap: Theory, numerical techniques, and applications journal, January 2019

Exploring 2-Group Global Symmetries text, January 2018

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

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

Correlators of Mixed Symmetry Operators in Defect CFTs text, January 2018

Topological censorship
journal, September 1993

Constraints on parity violating conformal field theories in d = 3
journal, November 2017

Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions
journal, March 2016

On superconformal characters and partition functions in three dimensions
journal, February 2010

Limits on massless particles
journal, October 1980

Aspects of superconformal multiplets in D > 4
journal, November 2016

Averaged null energy condition from causality
journal, July 2017

Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009

AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound
journal, March 2010

Spectral sum rules for conformal field theories in arbitrary dimensions
journal, July 2017

Spinning conformal correlators
journal, November 2011

Nonpositivity of the energy density in quantized field theories
journal, April 1965

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

General bootstrap equations in 4D CFTs
journal, January 2018

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

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

On conformal field theories with extremal $ \frac{a}{c} $ values
journal, April 2014

Counting conformal correlators
journal, February 2018

Two-point functions of conformal primary operators in N $$ \mathcal{N} $$ = 1 superconformal theories
journal, October 2014

Conformal collider physics: energy and charge correlations
journal, May 2008

On short and semi-short representations for four-dimensional superconformal symmetry
journal, September 2003

Holographic GB gravity in arbitrary dimensions
journal, March 2010

General three-point functions in 4D CFT
journal, January 2015

Bounds on OPE coefficients from interference effects in the conformal collider
journal, November 2017

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

On Superconformal Characters and Partition Functions in Three Dimensions
text, January 2008

Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
text, January 2009

AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound
text, January 2009

Holographic GB gravity in arbitrary dimensions
text, January 2009

Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
text, January 2015

A Proof of the Conformal Collider Bounds
text, January 2016

Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
text, January 2016

Spectral sum rules for conformal field theories in arbitrary dimensions
text, January 2016

Counting Conformal Correlators
preprint, January 2016

On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
text, January 2002

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

Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren
journal, February 1977

A proof of the conformal collider bounds
journal, June 2016

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

On Conformal Field Theories With Extremal a/c Values
text, January 2013

Implications of ANEC for SCFTs in four dimensions
journal, January 2020

Exploring 2-group global symmetries
journal, February 2019

Higher spin ANEC and the space of CFTs
journal, July 2019

Correlators of mixed symmetry operators in defect CFTs
journal, October 2018

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

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019

Exploring 2-Group Global Symmetries
text, January 2018

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

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

Correlators of Mixed Symmetry Operators in Defect CFTs
text, January 2018