Fermion conformal bootstrap in 4d

Karateev, Denis; Kravchuk, Petr; Serone, Marco; Vichi, Alessandro

doi:10.1007/JHEP06(2019)088

Title: Fermion conformal bootstrap in 4d

Abstract

We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved “fake primary” effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks.

Authors:

^[1]; Kravchuk, Petr ^[2]; Serone, Marco ^[3]; Vichi, Alessandro ^[1]

Ecole Polytechnique Federale Lausanne (Switzlerland). Inst. of Physics
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
National Inst. of Nuclear Physics (INFN), Trieste (Italy); International School for Advanced Studies (SISSA), Trieste (Italy)

Publication Date:: Tue Jun 18 00:00:00 EDT 2019

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

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

OSTI Identifier:: 1596663

Grant/Contract Number:: SC0009988; PP00P2-163670

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: 2019; 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; Conformal Field Theory; Field Theories in Higher Dimensions; Nonperturbative Effects

Citation Formats


                    Karateev, Denis, Kravchuk, Petr, Serone, Marco, and Vichi, Alessandro. Fermion conformal bootstrap in 4d.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP06(2019)088.

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                    Karateev, Denis, Kravchuk, Petr, Serone, Marco, & Vichi, Alessandro. Fermion conformal bootstrap in 4d.  United States.  https://doi.org/10.1007/JHEP06(2019)088

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                    Karateev, Denis, Kravchuk, Petr, Serone, Marco, and Vichi, Alessandro. Tue .  
"Fermion conformal bootstrap in 4d".  United States.  https://doi.org/10.1007/JHEP06(2019)088.  https://www.osti.gov/servlets/purl/1596663.

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@article{osti_1596663,

  title        = {Fermion conformal bootstrap in 4d},

  author       = {Karateev, Denis and Kravchuk, Petr and Serone, Marco and Vichi, Alessandro},

  abstractNote = {We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved “fake primary” effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks.},

  doi          = {10.1007/JHEP06(2019)088},

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

  number       = 6,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Jun 18 00:00:00 EDT 2019},

  month        = {Tue Jun 18 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referenced in this record:

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Similar Records

Title: Fermion conformal bootstrap in 4d

Abstract

Citation Formats

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

Bootstrap bound for conformal multi-flavor QCD on lattice journal, July 2016

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

The analytic bootstrap and AdS superhorizon locality journal, December 2013

Casimir recursion relations for general conformal blocks journal, February 2018

Spinning conformal blocks journal, November 2011

Extremal bootstrapping: go with the flow journal, March 2018

Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order journal, July 1974

Spinning conformal correlators journal, November 2011

Analyticity in spin in conformal theories journal, September 2017

Bootstrapping 3D fermions with global symmetries journal, January 2018

Recursion relations for conformal blocks journal, September 2016

Seed conformal blocks in 4D CFT journal, February 2016

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

Counting conformal correlators journal, February 2018

The 3d stress-tensor bootstrap journal, February 2018

Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach journal, May 2016

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

A semidefinite program solver for the conformal bootstrap journal, June 2015

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

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap journal, April 2017

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

A spacetime derivation of the Lorentzian OPE inversion formula journal, July 2018

Bootstrapping 3D fermions journal, March 2016

Finite-component field representations of the conformal group journal, June 1969

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

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

Projectors and seed conformal blocks for traceless mixed-symmetry tensors journal, July 2016

Weight shifting operators and conformal blocks journal, February 2018

Precision islands in the Ising and O(N ) models journal, August 2016

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

Convexity and liberation at large spin journal, November 2013

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

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

On the phase structure of vector-like gauge theories with massless fermions journal, March 1982

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

Covariant approaches to superconformal blocks journal, August 2014

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

Projectors, shadows, and conformal blocks journal, April 2014

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

Bootstrapping mixed correlators in the 3D Ising model journal, November 2014

Lattice tests of beyond standard model dynamics journal, January 2016

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

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

The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices journal, February 2019

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

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

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

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

Spinning Conformal Blocks text, January 2011

Projectors, Shadows, and Conformal Blocks text, January 2012

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

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

Covariant Approaches to Superconformal Blocks text, January 2014

Bootstrapping Mixed Correlators in the 3D Ising Model text, January 2014

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

Deconstructing Conformal Blocks in 4D CFT preprint, January 2015

Bootstrapping 3D Fermions text, January 2015

Seed Conformal Blocks in 4D CFT text, January 2016

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

Counting Conformal Correlators preprint, January 2016

Notes on Spinning Operators in Fermionic CFT text, January 2017

Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs text, January 2017

Analyticity in Spin in Conformal Theories text, January 2017

Bootstrapping 3D Fermions with Global Symmetries text, January 2017

Weight Shifting Operators and Conformal Blocks text, January 2017

The 3d Stress-Tensor Bootstrap text, January 2017

Casimir recursion relations for general conformal blocks text, January 2017

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

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

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

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

Bootstrap bound for conformal multi-flavor QCD on lattice
journal, July 2016

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

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Casimir recursion relations for general conformal blocks
journal, February 2018

Spinning conformal blocks
journal, November 2011

Extremal bootstrapping: go with the flow
journal, March 2018

Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order
journal, July 1974

Spinning conformal correlators
journal, November 2011

Analyticity in spin in conformal theories
journal, September 2017

Bootstrapping 3D fermions with global symmetries
journal, January 2018

Recursion relations for conformal blocks
journal, September 2016

Seed conformal blocks in 4D CFT
journal, February 2016

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

Counting conformal correlators
journal, February 2018

The 3d stress-tensor bootstrap
journal, February 2018

Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
journal, May 2016

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

A semidefinite program solver for the conformal bootstrap
journal, June 2015

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

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap
journal, April 2017

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

A spacetime derivation of the Lorentzian OPE inversion formula
journal, July 2018

Bootstrapping 3D fermions
journal, March 2016

Finite-component field representations of the conformal group
journal, June 1969

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

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

Projectors and seed conformal blocks for traceless mixed-symmetry tensors
journal, July 2016

Weight shifting operators and conformal blocks
journal, February 2018

Precision islands in the Ising and O(N ) models
journal, August 2016

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

Convexity and liberation at large spin
journal, November 2013

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

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

On the phase structure of vector-like gauge theories with massless fermions
journal, March 1982

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

Covariant approaches to superconformal blocks
journal, August 2014

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

Projectors, shadows, and conformal blocks
journal, April 2014

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

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

Lattice tests of beyond standard model dynamics
journal, January 2016

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

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

The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices
journal, February 2019

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

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

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

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

Spinning Conformal Blocks
text, January 2011

Projectors, Shadows, and Conformal Blocks
text, January 2012

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

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

Covariant Approaches to Superconformal Blocks
text, January 2014

Bootstrapping Mixed Correlators in the 3D Ising Model
text, January 2014

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

Deconstructing Conformal Blocks in 4D CFT
preprint, January 2015

Bootstrapping 3D Fermions
text, January 2015

Seed Conformal Blocks in 4D CFT
text, January 2016

Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
text, January 2016

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

Counting Conformal Correlators
preprint, January 2016

Notes on Spinning Operators in Fermionic CFT
text, January 2017

Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
text, January 2017

Analyticity in Spin in Conformal Theories
text, January 2017

Bootstrapping 3D Fermions with Global Symmetries
text, January 2017

Weight Shifting Operators and Conformal Blocks
text, January 2017

The 3d Stress-Tensor Bootstrap
text, January 2017

Casimir recursion relations for general conformal blocks
text, January 2017

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

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

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