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

Journal Article · · Journal of High Energy Physics (Online)
 [1]
  1. Inst. for Advanced Study, Princeton, NJ (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
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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.

Research Organization:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0009988
OSTI ID:
1597784
Journal Information:
Journal of High Energy Physics (Online), Vol. 2017, Issue 3; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 158 works
Citation information provided by
Web of Science

References (81)

Carving out the space of 4D CFTs journal May 2012
Bootstrap bound for conformal multi-flavor QCD on lattice journal July 2016
The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap journal March 2016
Eikonalization of conformal blocks journal September 2015
Bootstrapping the O(N ) vector models journal June 2014
Causality constraints in conformal field theory journal May 2016
The analytic bootstrap and AdS superhorizon locality journal December 2013
More on analytic bootstrap for O(N) models journal June 2016
ϕ 3 theory with F4 flavor symmetry in 6 − 2ϵ dimensions: 3-loop renormalization and conformal bootstrap journal December 2016
Bootstrapping the 3d Ising twist defect journal March 2014
Remarks on the convergence properties of the conformal block expansion journal February 2016
The bootstrap program for boundary CFT d journal July 2013
A new spin on causality constraints journal October 2016
Conformal bootstrap with slightly broken higher spin symmetry journal June 2016
Non-gaussianity of the critical 3d Ising model journal January 2017
A semidefinite program solver for the conformal bootstrap journal June 2015
Critical exponents of the 3d Ising and related models from conformal bootstrap journal October 2014
Tensor representations of conformal algebra and conformally covariant operator product expansion journal March 1973
Conformal partial waves and the operator product expansion journal February 2004
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents journal June 2014
Analytic bootstrap at large spin journal November 2015
Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions journal March 2016
Scalar-vector bootstrap journal January 2016
Improved bounds for CFT’s with global symmetries journal January 2012
Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4 journal May 2016
Precision islands in the Ising and O(N ) models journal August 2016
Convexity and liberation at large spin journal November 2013
Boundary and interface CFTs from the conformal bootstrap journal May 2015
Bounding scalar operator dimensions in 4 D CFT journal December 2008
The superconformal bootstrap for structure constants journal September 2014
Dimensional reduction for conformal blocks journal September 2016
The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions journal September 2014
Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators journal January 2016
Unitarity and the holographic S-Matrix journal October 2012
Bounds on OPE coefficients in 4D Conformal Field Theories journal October 2014
Bootstrapping mixed correlators in the 3D Ising model journal November 2014
Comments on operators with large spin journal November 2007
Accidental symmetries and the conformal bootstrap journal January 2016
Conformal Bootstrap in Mellin Space journal February 2017
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
Constraints on Conformal Field Theories in Diverse Dimensions from the Bootstrap Mechanism journal October 2013
Bounding the space of holographic CFTs with chaos journal October 2016
Universal anomalous dimensions at large spin and large twist journal July 2015
Towards bootstrapping QED3 journal August 2016
Bootstrapping 3D fermions journal March 2016
Bootstrapping the O(N) archipelago journal November 2015
A bound on chaos journal August 2016
Bounds on 4D conformal and superconformal field theories journal May 2011
Looking for a bulk point journal January 2017
Bootstrapping Conformal Field Theories with the Extremal Functional Method journal December 2013
A proof of the conformal collider bounds journal June 2016
Implications of Conformal Invariance in Field Theories for General Dimensions journal May 1994
On the Uniqueness of Higher-Spin Symmetries in ads and cft journal December 2013
Bounds on N $$ \mathcal{N} $$ = 1 superconformal theories with global symmetries journal August 2014
Conformal four point functions and the operator product expansion journal April 2001
Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion text January 1971
All unitary ray representations of the conformal group SU(2,2) with positive energy text January 1975
Bounds on 4D Conformal and Superconformal Field Theories text January 2010
The Bootstrap Program for Boundary CFT_d text January 2012
Bootstrapping Conformal Field Theories with the Extremal Functional Method text January 2012
On the uniqueness of higher-spin symmetries in AdS and CFT text January 2013
Bootstrapping the O(N) Vector Models text January 2013
Bootstrapping the 3d Ising twist defect text January 2013
Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents text January 2014
Critical exponents of the 3d Ising and related models from Conformal Bootstrap 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
A bound on chaos text January 2015
Universal anomalous dimensions at large spin and large twist text January 2015
Eikonalization of Conformal Blocks text January 2015
Bootstrapping 3D Fermions text January 2015
Scalar-Vector Bootstrap text January 2015
Causality Constraints in Conformal Field Theory text January 2015
Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions text January 2015
Remarks on the Convergence Properties of the Conformal Block Expansion text January 2015
Towards Bootstrapping QED$_3$ text January 2016
More on analytic bootstrap for O(N) models text January 2016
Bounding the Space of Holographic CFTs with Chaos text January 2016
A Proof of the Conformal Collider Bounds text January 2016
Precision Islands in the Ising and $O(N)$ Models text January 2016
Non-gaussianity of the critical 3d Ising model text January 2016

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Propagator identities, holographic conformal blocks, and higher-point AdS diagrams journal October 2019
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Inverse bootstrapping conformal field theories journal January 2018
A scaling theory for the long-range to short-range crossover and an infrared duality journal August 2017
On the Polyakov-Mellin bootstrap journal December 2018
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
A Mellin space approach to the conformal bootstrap journal May 2017
Thermal CFTs in momentum space journal January 2020
Universality at large transverse spin in defect CFT text January 2018
Higher spin ANEC and the space of CFTs journal July 2019
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory journal July 2018
Conformal bootstrap at large charge journal May 2018
Gravitational S-matrix from CFT dispersion relations journal December 2018
Bootstrapping the long-range Ising model in three dimensions journal January 2019
Long multiplet bootstrap text January 2017
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory text January 2018
Analyticity in Spin in Conformal Theories text January 2017
Long-range critical exponents near the short-range crossover text January 2017
Holographic Reconstruction of AdS Exchanges from Crossing Symmetry text January 2017
Bootstrapping 3D Fermions with Global Symmetries text January 2017
The 3d Stress-Tensor Bootstrap text January 2017
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory text January 2017
Solving M-theory with the Conformal Bootstrap text January 2017
Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE text January 2017
The Conformal Bootstrap at Finite Temperature text January 2018
Light-ray operators in conformal field theory text January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text January 2018
Anomalous Dimensions from Crossing Kernels text January 2018
Momentum-space conformal blocks on the light cone text January 2018
A Study of Quantum Field Theories in AdS at Finite Coupling text January 2018
Bootstrapping the long-range Ising model in three dimensions text January 2018
Polyakov-Mellin Bootstrap for AdS loops text January 2018
Fast Conformal Bootstrap and Constraints on 3d Gravity text January 2019
Thermal CFTs in momentum space text January 2019
Closed-form expression for cross-channel conformal blocks near the lightcone text January 2019
An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$ text January 2019
Monte Carlo study of an improved clock model in three dimensions text January 2019

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