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Title: The lightcone bootstrap and the spectrum of the 3d Ising CFT

Abstract

In this paper. we compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2,R) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial data $$\{\Delta_\sigma,\Delta_\epsilon,f_{\sigma\sigma\epsilon},f_{\epsilon\epsilon\epsilon},c_T\}$$. The analytic results agree with numerics to high precision for about 100 low-twist operators (correctly accounting for O(1) mixing effects between large-spin families). Plugging these results back into the crossing equations, we obtain approximate analytic constraints on the initial data.

Authors:
 [1]
  1. Inst. for Advanced Study, Princeton, NJ (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1597784
Grant/Contract Number:  
SC0009988
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2017; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Simmons-Duffin, David. The lightcone bootstrap and the spectrum of the 3d Ising CFT. United States: N. p., 2017. Web. doi:10.1007/JHEP03(2017)086.
Simmons-Duffin, David. The lightcone bootstrap and the spectrum of the 3d Ising CFT. United States. doi:10.1007/JHEP03(2017)086.
Simmons-Duffin, David. Wed . "The lightcone bootstrap and the spectrum of the 3d Ising CFT". United States. doi:10.1007/JHEP03(2017)086. https://www.osti.gov/servlets/purl/1597784.
@article{osti_1597784,
title = {The lightcone bootstrap and the spectrum of the 3d Ising CFT},
author = {Simmons-Duffin, David},
abstractNote = {In this paper. we compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2,R) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial data $\{\Delta_\sigma,\Delta_\epsilon,f_{\sigma\sigma\epsilon},f_{\epsilon\epsilon\epsilon},c_T\}$. The analytic results agree with numerics to high precision for about 100 low-twist operators (correctly accounting for O(1) mixing effects between large-spin families). Plugging these results back into the crossing equations, we obtain approximate analytic constraints on the initial data.},
doi = {10.1007/JHEP03(2017)086},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 3,
volume = 2017,
place = {United States},
year = {2017},
month = {3}
}

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Cited by: 83 works
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Works referenced in this record:

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984


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


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

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


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

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

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


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


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 superconformal bootstrap for structure constants
journal, September 2014


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

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

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

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


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

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

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

The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap
journal, March 2016

  • Beem, Christopher; Lemos, Madalena; Liendo, Pedro
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)183

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


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

Accidental symmetries and the conformal bootstrap
journal, January 2016

  • Chester, Shai M.; Giombi, Simone; Iliesiu, Luca V.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)110

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

Scalar-vector bootstrap
journal, January 2016

  • Rejon-Barrera, Fernando; Robbins, Daniel
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)139

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators
journal, January 2016


Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4
journal, May 2016

  • Chester, Shai M.; Iliesiu, Luca V.; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)103

Towards bootstrapping QED3
journal, August 2016

  • Chester, Shai M.; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)019

More on analytic bootstrap for O(N) models
journal, June 2016

  • Dey, Parijat; Kaviraj, Apratim; Sen, Kallol
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)136

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


ϕ 3 theory with F4 flavor symmetry in 6 − 2ϵ dimensions: 3-loop renormalization and conformal bootstrap
journal, December 2016

  • Pang, Yi; Rong, Junchen; Su, Ning
  • Journal of High Energy Physics, Vol. 2016, Issue 12
  • DOI: 10.1007/JHEP12(2016)057

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


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

Conformal Bootstrap in Mellin Space
journal, February 2017


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

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

Conformal bootstrap with slightly broken higher spin symmetry
journal, June 2016

  • Alday, Luis F.; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)091

Analytic bootstrap at large spin
journal, November 2015

  • Kaviraj, Apratim; Sen, Kallol; Sinha, Aninda
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)083

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

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

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


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


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


Comments on operators with large spin
journal, November 2007


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

Bounding the space of holographic CFTs with chaos
journal, October 2016


Dimensional reduction for conformal blocks
journal, September 2016


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

On the Uniqueness of Higher-Spin Symmetries in ads and cft
journal, December 2013

  • Boulanger, N.; Ponomarev, D.; Skvortsov, E.
  • International Journal of Modern Physics A, Vol. 28, Issue 31
  • DOI: 10.1142/S0217751X13501625

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


Remarks on the convergence properties of the conformal block expansion
journal, February 2016


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

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

Looking for a bulk point
journal, January 2017

  • Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2017, Issue 1
  • DOI: 10.1007/JHEP01(2017)013

A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

Causality constraints in conformal field theory
journal, May 2016

  • Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)099

A new spin on causality constraints
journal, October 2016

  • Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/JHEP10(2016)141

A proof of the conformal collider bounds
journal, June 2016

  • Hofman, Diego M.; Li, Daliang; Meltzer, David
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)111

Non-gaussianity of the critical 3d Ising model
journal, January 2017


    Works referencing / citing this record:

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

    • Mazáč, Dalimil; Paulos, Miguel F.
    • Journal of High Energy Physics, Vol. 2019, Issue 2
    • DOI: 10.1007/jhep02(2019)163

    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

    AdS4/CFT3 for unprotected operators
    journal, July 2018


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


    Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
    text, January 2017

    • Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2017-11690

    Bootstrapping the (A1, A2) Argyres-Douglas theory
    journal, March 2018

    • Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
    • Journal of High Energy Physics, Vol. 2018, Issue 3
    • DOI: 10.1007/jhep03(2018)033