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Title: Bootstrapping the O(N) archipelago

Abstract

We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector Φi and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (Δ Φ , Δ s ) to lie inside small islands. Here, we also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.

Authors:
 [1];  [1];  [2];  [3]
  1. Yale Univ., New Haven, CT (United States)
  2. Institute for Advanced Study, Princeton, NJ (United States)
  3. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Publication Date:
Research Org.:
Yale Univ., New Haven, CT (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1435150
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: 2015; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Global Symmetries

Citation Formats

Kos, Filip, Poland, David, Simmons-Duffin, David, and Vichi, Alessandro. Bootstrapping the O(N) archipelago. United States: N. p., 2015. Web. doi:10.1007/JHEP11(2015)106.
Kos, Filip, Poland, David, Simmons-Duffin, David, & Vichi, Alessandro. Bootstrapping the O(N) archipelago. United States. doi:https://doi.org/10.1007/JHEP11(2015)106
Kos, Filip, Poland, David, Simmons-Duffin, David, and Vichi, Alessandro. Tue . "Bootstrapping the O(N) archipelago". United States. doi:https://doi.org/10.1007/JHEP11(2015)106. https://www.osti.gov/servlets/purl/1435150.
@article{osti_1435150,
title = {Bootstrapping the O(N) archipelago},
author = {Kos, Filip and Poland, David and Simmons-Duffin, David and Vichi, Alessandro},
abstractNote = {We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector Φi and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (Δ Φ , Δ s ) to lie inside small islands. Here, we also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.},
doi = {10.1007/JHEP11(2015)106},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2015,
place = {United States},
year = {2015},
month = {11}
}

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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

Eikonalization of conformal blocks
journal, September 2015

  • Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)019

Specific heat of liquid helium in zero gravity very near the lambda point
journal, November 2003


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

Five dimensional <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-symmetric CFTs from conformal bootstrap
journal, June 2014


Eliminating leading corrections to scaling in the three-dimensional O ( N )-symmetric ϕ 4 model: N = 3 and 4
journal, October 2001


Constraints on Conformal Field Theories in Diverse Dimensions from the Bootstrap Mechanism
journal, October 2013


Bootstrapping the 3d Ising twist defect
journal, March 2014

  • Gaiotto, Davide; Mazac, Dalimil; Paulos, Miguel F.
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)100

The bootstrap program for boundary CFT d
journal, July 2013

  • Liendo, Pedro; Rastelli, Leonardo; van Rees, Balt C.
  • Journal of High Energy Physics, Vol. 2013, Issue 7
  • DOI: 10.1007/JHEP07(2013)113

Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography
journal, December 2014


Universal anomalous dimensions at large spin and large twist
journal, July 2015

  • Kaviraj, Apratim; Sen, Kallol; Sinha, Aninda
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)026

More holography from conformal field theory
journal, September 2010


Critical exponents of the 3d Ising and related models from conformal bootstrap
journal, October 2014

  • Gliozzi, Ferdinando; Rago, Antonio
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)042

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


Holography from conformal field theory
journal, October 2009


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

  • El-Showk, Sheer; Paulos, Miguel F.; Poland, David
  • Journal of Statistical Physics, Vol. 157, Issue 4-5
  • DOI: 10.1007/s10955-014-1042-7

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

  • Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea
  • Physical Review B, Vol. 65, Issue 14
  • DOI: 10.1103/PhysRevB.65.144520

Universal Conductivity in a Two-Dimensional Superfluid-to-Insulator Quantum Critical System
journal, January 2014


Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

  • Beem, Christopher; Lemos, Madalena; Liendo, Pedro
  • Communications in Mathematical Physics, Vol. 336, Issue 3
  • DOI: 10.1007/s00220-014-2272-x

Critical Capacitance and Charge-Vortex Duality Near the Superfluid-to-Insulator Transition
journal, December 2014


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


Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

  • Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)145

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


The dynamics of quantum criticality revealed by quantum Monte Carlo and holography
journal, March 2014

  • Witczak-Krempa, William; Sørensen, Erik S.; Sachdev, Subir
  • Nature Physics, Vol. 10, Issue 5
  • DOI: 10.1038/nphys2913

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

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


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

Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition
journal, October 2005


Boundary and interface CFTs from the conformal bootstrap
journal, May 2015

  • Gliozzi, Ferdinando; Liendo, Pedro; Meineri, Marco
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)036

Critical phenomena and renormalization-group theory
journal, October 2002


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


W $$ \mathcal{W} $$ symmetry in six dimensions
journal, May 2015

  • Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)017

The superconformal bootstrap for structure constants
journal, September 2014


N = 4 Superconformal Bootstrap
journal, August 2013


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


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


Emergent spacetime and holographic CFTs
journal, October 2012

  • El-Showk, Sheer; Papadodimas, Kyriakos
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)106

Exact correlators of BPS Operators from the 3d superconformal bootstrap
journal, March 2015

  • Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)130

Universal conductivity of two-dimensional films at the superconductor-insulator transition
journal, October 1991

  • Cha, Min-Chul; Fisher, Matthew P. A.; Girvin, S. M.
  • Physical Review B, Vol. 44, Issue 13
  • DOI: 10.1103/PhysRevB.44.6883

The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions
journal, September 2014

  • Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)143

Conformal Field Theories in Fractional Dimensions
journal, April 2014


Bounds on N $$ \mathcal{N} $$ = 1 superconformal theories with global symmetries
journal, August 2014

  • Berkooz, Micha; Yacoby, Ran; Zait, Amir
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)008

Lessons from crossing symmetry at large N
journal, June 2015

  • Alday, Luis F.; Bissi, Agnese; Lukowski, Tomasz
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)074

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

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

  • Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea
  • Physical Review B, Vol. 74, Issue 14
  • DOI: 10.1103/PhysRevB.74.144506

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

Bootstrapping the Three Dimensional Supersymmetric Ising Model
journal, July 2015


    Works referencing / citing this record:

    Solving M-theory with the conformal bootstrap
    journal, June 2018

    • Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
    • Journal of High Energy Physics, Vol. 2018, Issue 6
    • DOI: 10.1007/jhep06(2018)159

    Solving M-theory with the conformal bootstrap
    journal, June 2018

    • Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
    • Journal of High Energy Physics, Vol. 2018, Issue 6
    • DOI: 10.1007/jhep06(2018)159

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

    • De Polsi, Gonzalo; Tissier, Matthieu; Wschebor, Nicolás
    • Journal of Statistical Physics, Vol. 177, Issue 6
    • DOI: 10.1007/s10955-019-02411-3

    Optical Conductivity of Topological Surface States with Emergent Supersymmetry
    journal, March 2016


    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

    Inverse bootstrapping conformal field theories
    journal, January 2018


    Anomalous dimensions of spinning operators from conformal symmetry
    journal, January 2018


    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

    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

    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

    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

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


    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

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


    Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey
    journal, March 2018

    • Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan
    • Journal of High Energy Physics, Vol. 2018, Issue 3
    • DOI: 10.1007/jhep03(2018)123

    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

    Compensating strong coupling with large charge
    journal, April 2017

    • Alvarez-Gaume, Luis; Loukas, Orestis; Orlando, Domenico
    • Journal of High Energy Physics, Vol. 2017, Issue 4
    • DOI: 10.1007/jhep04(2017)059

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


    An algebraic approach to the analytic bootstrap
    journal, April 2017

    • Alday, Luis F.; Zhiboedov, Alexander
    • Journal of High Energy Physics, Vol. 2017, Issue 4
    • DOI: 10.1007/jhep04(2017)157

    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

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


    3d Abelian gauge theories at the boundary
    journal, May 2019

    • Di Pietro, Lorenzo; Gaiotto, Davide; Lauria, Edoardo
    • Journal of High Energy Physics, Vol. 2019, Issue 5
    • DOI: 10.1007/jhep05(2019)091

    Charting the space of 3D CFTs with a continuous global symmetry
    journal, May 2019

    • Dymarsky, Anatoly; Penedones, Joao; Trevisani, Emilio
    • Journal of High Energy Physics, Vol. 2019, Issue 5
    • DOI: 10.1007/jhep05(2019)098

    autoboot: a generator of bootstrap equations with global symmetry
    journal, June 2019


    Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
    journal, July 2018

    • Isachenkov, Mikhail; Schomerus, Volker
    • Journal of High Energy Physics, Vol. 2018, Issue 7
    • DOI: 10.1007/jhep07(2018)180

    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

    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

    The effective bootstrap
    journal, September 2016

    • Echeverri, Alejandro Castedo; von Harling, Benedict; Serone, Marco
    • Journal of High Energy Physics, Vol. 2016, Issue 9
    • DOI: 10.1007/jhep09(2016)097

    Scalar CFTs and their large N limits
    journal, September 2018


    Bootstrapping the spectral function: on the uniqueness of Liouville and the universality of BTZ
    journal, September 2018

    • Collier, Scott; Kravchuk, Petr; Lin, Ying-Hsuan
    • Journal of High Energy Physics, Vol. 2018, Issue 9
    • DOI: 10.1007/jhep09(2018)150

    Truncatable bootstrap equations in algebraic form and critical surface exponents
    journal, October 2016


    The conformal bootstrap at finite temperature
    journal, October 2018

    • Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu
    • Journal of High Energy Physics, Vol. 2018, Issue 10
    • DOI: 10.1007/jhep10(2018)070

    A note on inhomogeneous ground states at large global charge
    journal, October 2019

    • Hellerman, Simeon; Kobayashi, Nozomu; Maeda, Shunsuke
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)038

    O(N) and O(N) and O(N)
    journal, November 2017

    • Gubser, Steven S.; Jepsen, Christian; Parikh, Sarthak
    • Journal of High Energy Physics, Vol. 2017, Issue 11
    • DOI: 10.1007/jhep11(2017)107

    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

    Superconformal blocks for mixed 1/2-BPS correlators with SU(2) R-symmetry
    journal, November 2019

    • Baume, Florent; Fuchs, Michael; Lawrie, Craig
    • Journal of High Energy Physics, Vol. 2019, Issue 11
    • DOI: 10.1007/jhep11(2019)164

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


    The conformal bootstrap
    journal, June 2016

    • Poland, David; Simmons-Duffin, David
    • Nature Physics, Vol. 12, Issue 6
    • DOI: 10.1038/nphys3761

    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

    Bootstrapping the long-range Ising model in three dimensions
    journal, January 2019


    Vortex-loop calculation of the specific heat of superfluid He 4 under pressure
    journal, December 2019


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


    Dynamical Response near Quantum Critical Points
    journal, February 2017


    Conformal Dimensions via Large Charge Expansion
    journal, February 2018


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


    Bootstrap experiments on higher dimensional CFTs
    journal, March 2018


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


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