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Title: Analytic and numerical bootstrap of CFTs with $$O(m)\times O(n)$$ global symmetry in 3D

Abstract

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 − d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. University of Oxford
  2. University of Crete
  3. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC); USDOE Laboratory Directed Research and Development (LDRD) Program; Simons Foundation
OSTI Identifier:
1659334
Alternate Identifier(s):
OSTI ID: 1711393
Report Number(s):
LA-UR-20-23147
Journal ID: ISSN 2542-4653; 035
Grant/Contract Number:  
89233218CNA000001; AC02-05CH11231; 48865; 20180709PRD1
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 9 Journal Issue: 3; Journal ID: ISSN 2542-4653
Publisher:
SciPost Foundation
Country of Publication:
Netherlands
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Henriksson, Johan, Kousvos, Stefanos R., and Stergiou, Andreas. Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D. Netherlands: N. p., 2020. Web. doi:10.21468/SciPostPhys.9.3.035.
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Henriksson, Johan, Kousvos, Stefanos R., & Stergiou, Andreas. Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D. Netherlands. https://doi.org/10.21468/SciPostPhys.9.3.035
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Henriksson, Johan, Kousvos, Stefanos R., and Stergiou, Andreas. Thu . "Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D". Netherlands. https://doi.org/10.21468/SciPostPhys.9.3.035.
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@article{osti_1659334,
title = {Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D},
author = {Henriksson, Johan and Kousvos, Stefanos R. and Stergiou, Andreas},
abstractNote = {Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 − d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.},
doi = {10.21468/SciPostPhys.9.3.035},
journal = {SciPost Physics Proceedings},
number = 3,
volume = 9,
place = {Netherlands},
year = {2020},
month = {9}
}
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Works referenced in this record:

1/n Expansion: Calculation of the exponents ? and? in the order 1/n2 for arbitrary number of dimensions
journal, June 1981

  • Vasil'ev, A. N.; Pis'mak, Yu. M.; Khonkonen, Yu. R.
  • Theoretical and Mathematical Physics, Vol. 47, Issue 3
  • DOI: 10.1007/BF01019296

Five-loop ϵ expansion for O(n)×O(m) spin models
journal, February 2004

Coleman-Weinberg symmetry breaking in the chiral SU(n) × SU(n) linear σ model
journal, July 1981

Critical behavior of linear Φ 4 models with G × G ′ symmetry
journal, April 1981

Multicritical behavior in frustrated spin systems with non-collinear order
journal, March 2005

The $\epsilon $-expansion from conformal field theory
journal, July 2015

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

Bootstrapping mixed correlators in three-dimensional cubic theories
journal, January 2019

Critical behavior of the mn-component field model in three dimensions II. Three-loop results
journal, December 1989

Normal-to-planar superfluid transition in He 3
journal, December 2004

Critical thermodynamics of three-dimensional MN -component field model with cubic anisotropy from higher-loop ε expansion
journal, May 2001

Renormalization-group analysis of chiral transitions
journal, September 1988

Critical O( N ) model to order ϵ 4 from analytic bootstrap
journal, December 2018

  • Henriksson, Johan; van Loon, Mark
  • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 2
  • DOI: 10.1088/1751-8121/aaf1e2

Critical behavior of frustrated spin models with noncollinear order
journal, March 2001

Taming the ϵ-expansion with large spin perturbation theory
journal, July 2018

  • Alday, Luis F.; Henriksson, Johan; van Loon, Mark
  • Journal of High Energy Physics, Vol. 2018, Issue 7
  • DOI: 10.1007/JHEP07(2018)131

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2
journal, January 2020

  • Alday, Luis F.; Henriksson, Johan; van Loon, Mark
  • Journal of High Energy Physics, Vol. 2020, Issue 1
  • DOI: 10.1007/JHEP01(2020)063

Analyticity in spin in conformal theories
journal, September 2017

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
journal, September 2010

Monte Carlo renormalization‐group studies of critical phenomena
journal, March 1982

  • Swendsen, Robert H.
  • Journal of Applied Physics, Vol. 53, Issue 3
  • DOI: 10.1063/1.330668

Frustrated Heisenberg Magnets: A Nonperturbative Approach
journal, May 2000

Critical exponent ω at O(1/N) in O(N)×O(m) spin models
journal, November 2002

Monte Carlo study of the critical properties of noncollinear Heisenberg magnets: O ( 3 ) × O ( 2 ) universality class
journal, December 2019

Large-n critical behavior of O(n)×O(m) spin models
journal, July 2001

3D CFT archipelago from single correlator bootstrap
journal, October 2019

Bootstrapping the minimal 3D SCFT
journal, November 2018

  • Atanasov, Alexander; Hillman, Aaron; Poland, David
  • Journal of High Energy Physics, Vol. 2018, Issue 11
  • DOI: 10.1007/JHEP11(2018)140

Deligne categories in lattice models and quantum field theory, or making sense of O(N) symmetry with non-integer N
journal, April 2020

Simple method of calculating the critical indices in the 1/n expansion
journal, February 1981

  • Vasil'ev, A. N.; Pis'mak, Yu. M.; Khonkonen, Yu. R.
  • Theoretical and Mathematical Physics, Vol. 46, Issue 2
  • DOI: 10.1007/BF01030844

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

Critical behavior of the mn-component field model in three dimensions
journal, November 1988

Large spin systematics in CFT
journal, November 2015

  • Alday, Luis F.; Bissi, Agnese; Lukowski, Tomasz
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)101

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

General properties of multiscalar RG Flows in $d=4-\varepsilon$
journal, January 2019

Large Spin Perturbation Theory for Conformal Field Theories
journal, September 2017

Bootstrapping the O(N) archipelago
journal, November 2015

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)106

Bootstrapping hypercubic and hypertetrahedral theories in three dimensions
journal, May 2018

Carving out OPE space and precise O(2) model critical exponents
journal, June 2020

  • Chester, Shai M.; Landry, Walter; Liu, Junyu
  • Journal of High Energy Physics, Vol. 2020, Issue 6
  • DOI: 10.1007/JHEP06(2020)142

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

Bootstrapping MN and tetragonal CFTs in three dimensions
journal, January 2019

Critical behavior of O ( 2 ) ⊗ O ( N ) symmetric models
journal, November 2004

  • Calabrese, Pasquale; Parruccini, Pietro; Pelissetto, Andrea
  • Physical Review B, Vol. 70, Issue 17
  • DOI: 10.1103/PhysRevB.70.174439

Mellin space bootstrap for global symmetry
journal, July 2017

  • Dey, Parijat; Kaviraj, Apratim; Sinha, Aninda
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)019

Bootstrapping mixed correlators in three-dimensional cubic theories II
journal, January 2020

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

A Mellin space approach to the conformal bootstrap
journal, May 2017

  • Gopakumar, Rajesh; Kaviraj, Apratim; Sen, Kallol
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)027

Critical phenomena and renormalization-group theory
journal, October 2002

Generalized Chiral Universality
journal, July 1990

  • Kawamura, Hikaru
  • Journal of the Physical Society of Japan, Vol. 59, Issue 7
  • DOI: 10.1143/JPSJ.59.2305

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

Critical behavior of certain antiferromagnets with complicated ordering: Four-loop ɛ -expansion analysis
journal, November 2001

Remarks on the chiral phase transition in chromodynamics
journal, January 1984

Determining the order of chiral phase transition in QCD from conformal bootstrap
conference, July 2016

  • Nakayama, Yu
  • Proceedings of The 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)
  • DOI: 10.22323/1.251.0002

Bootstrapping mixed correlators in the five dimensional critical O(N) models
journal, April 2017

Critical Exponents in 3.99 Dimensions
journal, January 1972

XY frustrated systems: Continuous exponents in discontinuous phase transitions
journal, April 2003

Chiral exponents in O ( N ) × O ( m ) spin models at O ( 1 / N 2 )
journal, October 2002

Bootstrapping phase transitions in QCD and frustrated spin systems
journal, January 2015

Unitarity and the holographic S-Matrix
journal, October 2012

  • Fitzpatrick, A. Liam; Kaplan, Jared
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)032

Revisiting the dilatation operator of the Wilson–Fisher fixed point
journal, July 2017

Renormalization-group fixed points of general n -vector models
journal, March 1984

Solving CFTs with weakly broken higher spin symmetry
journal, October 2017

Six-dimensional Landau-Ginzburg-Wilson theory
journal, January 2017

Seeking fixed points in multiple coupling scalar theories in the ε expansion
journal, May 2018

PyCFTBoot: A Flexible Interface for the Conformal Bootstrap
journal, May 2017

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

The renormalization group and the ε expansion
journal, August 1974

Gravitational S-matrix from CFT dispersion relations
journal, December 2018

  • Alday, Luis F.; Caron-Huot, Simon
  • Journal of High Energy Physics, Vol. 2018, Issue 12
  • DOI: 10.1007/JHEP12(2018)017

Non-perturbative renormalization flow in quantum field theory and statistical physics
journal, June 2002

Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models
journal, January 2020

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