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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:
ORCiD logo [1];  [2];  [3];  [1]
  1. Ecole Polytechnique Federale Lausanne (Switzlerland). Inst. of Physics
  2. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  3. National Inst. of Nuclear Physics (INFN), Trieste (Italy); International School for Advanced Studies (SISSA), Trieste (Italy)
Publication Date:
Research Org.:
Inst. for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Swiss National Science Foundation (SNSF); European Research Council (ERC); Simons Foundation
OSTI Identifier:
1596663
Grant/Contract Number:  
SC0009988; PP00P2-163670
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
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.
Karateev, Denis, Kravchuk, Petr, Serone, Marco, & Vichi, Alessandro. Fermion conformal bootstrap in 4d. United States. doi:10.1007/JHEP06(2019)088.
Karateev, Denis, Kravchuk, Petr, Serone, Marco, and Vichi, Alessandro. Tue . "Fermion conformal bootstrap in 4d". United States. doi:10.1007/JHEP06(2019)088. https://www.osti.gov/servlets/purl/1596663.
@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)},
issn = {1029-8479},
number = 6,
volume = 2019,
place = {United States},
year = {2019},
month = {6}
}

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Works referenced in this record:

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

  • Poland, David; Simmons-Duffin, David; Vichi, Alessandro
  • Journal of High Energy Physics, Vol. 2012, Issue 5
  • DOI: 10.1007/JHEP05(2012)110

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


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

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)091

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

  • Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)004

Casimir recursion relations for general conformal blocks
journal, February 2018


Spinning conformal blocks
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)154

Extremal bootstrapping: go with the flow
journal, March 2018

  • El-Showk, Sheer; Paulos, Miguel F.
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)148

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


Spinning conformal correlators
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)071

Analyticity in spin in conformal theories
journal, September 2017


Bootstrapping 3D fermions with global symmetries
journal, January 2018

  • Iliesiu, Luca; Kos, Filip; Poland, David
  • Journal of High Energy Physics, Vol. 2018, Issue 1
  • DOI: 10.1007/JHEP01(2018)036

Recursion relations for conformal blocks
journal, September 2016

  • Penedones, João; Trevisani, Emilio; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)070

Notes on spinning operators in fermionic CFT
journal, May 2017

  • Giombi, S.; Kirilin, V.; Skvortsov, E.
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)041

Seed conformal blocks in 4D CFT
journal, February 2016

  • Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)183

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

  • Kravchuk, Petr; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2018, Issue 11
  • DOI: 10.1007/JHEP11(2018)102

Counting conformal correlators
journal, February 2018

  • Kravchuk, Petr; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)096

The 3d stress-tensor bootstrap
journal, February 2018

  • Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)164

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


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


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

  • Simmons-Duffin, David; Stanford, Douglas; Witten, Edward
  • Journal of High Energy Physics, Vol. 2018, Issue 7
  • DOI: 10.1007/JHEP07(2018)085

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

  • Elkhidir, Emtinan; Karateev, Denis; Serone, Marco
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)133

Bootstrapping 3D fermions
journal, March 2016

  • Iliesiu, Luca; Kos, Filip; Poland, David
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)120

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


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


Deconstructing conformal blocks in 4D CFT
journal, August 2015

  • Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)101

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

  • Costa, Miguel S.; Hansen, Tobias; Penedones, João
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)018

Improved bounds for CFT’s with global symmetries
journal, January 2012


Weight shifting operators and conformal blocks
journal, February 2018

  • Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)081

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

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)036

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

  • Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)017

Convexity and liberation at large spin
journal, November 2013

  • Komargodski, Zohar; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)140

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


General bootstrap equations in 4D CFTs
journal, January 2018

  • Cuomo, Gabriel Francisco; Karateev, Denis; Kravchuk, Petr
  • Journal of High Energy Physics, Vol. 2018, Issue 1
  • DOI: 10.1007/JHEP01(2018)130

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

  • Mack, G.
  • Communications in Mathematical Physics, Vol. 55, Issue 1
  • DOI: 10.1007/BF01613145

Bootstrapping mixed correlators in 4D N $$ \mathcal{N} $$ = 1 SCFTs
journal, July 2017

  • Li, Daliang; Meltzer, David; Stergiou, Andreas
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)029

Covariant approaches to superconformal blocks
journal, August 2014

  • Fitzpatrick, A. Liam; Kaplan, Jared; Khandker, Zuhair U.
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)129

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

  • Caracciolo, Francesco; Echeverri, Alejandro Castedo; von Harling, Benedict
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)020

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

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)109

Lattice tests of beyond standard model dynamics
journal, January 2016


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