Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Carving out OPE space and precise O(2) model critical exponents

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4];  [2];  [5];  [6]
  1. Weizmann Inst. of Science, Rehovot (Israel). Dept. of Particle Physics and Astrophysics
  2. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  3. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics and Inst. for Quantum Information and Matter
  4. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Yale Univ., New Haven, CT (United States). Dept. of Physics
  5. Swiss Federal Inst. of Technology in Lausanne (EPFL) (Switzerland). Inst. of Physics
  6. Swiss Federal Inst. of Technology in Lausanne (EPFL) (Switzerland). Inst. of Physics; Univ. of Pisa (Italy). Dept. of Physics
+ Show Author Affiliations

We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.

Research Organization:
Yale Univ., New Haven, CT (United States); California Institute of Technology (CalTech), Pasadena, CA (United States); Swiss Federal Inst. of Technology in Lausanne (EPFL) (Switzerland)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Simons Foundation; European Research Council (ERC); Swiss National Science Foundation (SNSF)
Grant/Contract Number:
SC0020318; SC0019085; ACI-1548562; 488657; 488651; 758903; PP00P2-163670
OSTI ID:
1646617
Journal Information:
Journal of High Energy Physics (Online), Vol. 2020, Issue 6; ISSN 1029-8479
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

References (101)

Higher spin ANEC and the space of CFTs journal July 2019
High-precision measurement of the thermal exponent for the three-dimensional X Y universality class journal October 2006
Three ways to solve critical ϕ4 theory on 4 − 𝜖 dimensional real projective space: Perturbation, bootstrap, and Schwinger–Dyson equation journal March 2018
The quickhull algorithm for convex hulls journal December 1996
Bootstrap experiments on higher dimensional CFTs journal March 2018
N -component Ginzburg-Landau Hamiltonian with cubic anisotropy: A six-loop study journal June 2000
Bounding scalar operator dimensions in 4 D CFT journal December 2008
Universal constraints on conformal operator dimensions journal August 2009
The conformal bootstrap: Theory, numerical techniques, and applications journal January 2019
Bootstrapping mixed correlators in the 3D Ising model journal November 2014
Bootstrapping the O(N) archipelago journal November 2015
Precision islands in the Ising and O(N ) models journal August 2016
The M-theory archipelago journal February 2020
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap journal September 2016
Bootstrapping mixed correlators in 4D N $$ \mathcal{N} $$ = 1 SCFTs journal July 2017
Bootstrapping the long-range Ising model in three dimensions journal January 2019
Bootstrapping mixed correlators in three-dimensional cubic theories journal January 2019
Bootstrapping 3D fermions journal March 2016
Bootstrapping 3D fermions with global symmetries journal January 2018
Fermion conformal bootstrap in 4d journal June 2019
Charting the space of 3D CFTs with a continuous global symmetry journal May 2019
The 3d stress-tensor bootstrap journal February 2018
Bounds in 4D conformal field theories with global symmetry journal December 2010
Improved bounds for CFT’s with global symmetries journal January 2012
Carving out the space of 4D CFTs journal May 2012
Bootstrapping the O(N ) vector models journal June 2014
Bounds on N $$ \mathcal{N} $$ = 1 superconformal theories with global symmetries journal August 2014
Approaching the conformal window of O ( n ) × O ( m ) symmetric Landau-Ginzburg models using the conformal bootstrap journal June 2014
Bounds on OPE coefficients in 4D Conformal Field Theories journal October 2014
Bootstrapping phase transitions in QCD and frustrated spin systems journal January 2015
Bootstrapping O ( N ) vector models in 4 < d < 6 journal April 2015
Accidental symmetries and the conformal bootstrap journal January 2016
Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4 journal May 2016
Towards bootstrapping QED3 journal August 2016
Bootstrap bound for conformal multi-flavor QCD on lattice journal July 2016
Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach journal May 2016
Scalar CFTs and their large N limits journal September 2018
Monopole operators in U(1) Chern-Simons-matter theories journal May 2018
Bootstrapping hypercubic and hypertetrahedral theories in three dimensions journal May 2018
Solving the 3D Ising model with the conformal bootstrap journal July 2012
Bootstrapping the 3d Ising twist defect journal March 2014
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents journal June 2014
Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey journal March 2018
3D CFT archipelago from single correlator bootstrap journal October 2019
Bootstrapping MN and tetragonal CFTs in three dimensions journal January 2019
Bounds on 4D conformal and superconformal field theories journal May 2011
N = 4 Superconformal Bootstrap journal August 2013
Generalized bootstrap equations for N = 4 $$ \mathcal{N}=4 $$ SCFT journal February 2015
The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions journal September 2014
The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap journal March 2016
Bootstrapping SCFTs with four supercharges journal August 2015
The (2, 0) superconformal bootstrap journal January 2016
Exploring the minimal 4D N = 1 $$ \mathcal{N}=1 $$ SCFT journal December 2015
Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators journal January 2016
N $$ \mathcal{N} $$ = 4 superconformal bootstrap of the K3 CFT journal May 2017
(2, 2) superconformal bootstrap in two dimensions journal May 2017
3d N = 2 $$ \mathcal{N}=2 $$ minimal SCFTs from wrapped M5-branes journal August 2017
Bootstrapping N = 3 $$ \mathcal{N}=3 $$ superconformal theories journal April 2017
More N = 4 superconformal bootstrap journal August 2017
Long multiplet bootstrap journal October 2017
Carving out the end of the world or (superconformal bootstrap in six dimensions) journal August 2017
Bootstrapping the (A1, A2) Argyres-Douglas theory journal March 2018
Solving M-theory with the conformal bootstrap journal June 2018
Decoding a three-dimensional conformal manifold journal February 2018
Bootstrapping the half-BPS line defect journal October 2018
Bootstrapping the minimal 3D SCFT journal November 2018
Central charge bounds in 4D conformal field theory journal February 2011
Rigorous limits on the interaction strength in quantum field theory journal April 2010
The bootstrap program for boundary CFT d journal July 2013
Bootstrapping Conformal Field Theories with the Extremal Functional Method journal December 2013
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space journal April 2016
The effective bootstrap journal September 2016
Critical Ising model in varying dimension by conformal bootstrap journal January 2019
A semidefinite program solver for the conformal bootstrap journal June 2015
autoboot: a generator of bootstrap equations with global symmetry journal June 2019
Specific heat of liquid helium in zero gravity very near the lambda point journal November 2003
Monte Carlo study of an improved clock model in three dimensions journal December 2019
Anisotropic perturbations in three-dimensional O( N )-symmetric vector models journal September 2011
Gravity effects in fluids near the gas-liquid critical point journal January 1979
Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point journal February 1996
Specific Heat of Helium Confined to a 57- μ m Planar Geometry near the Lambda Point journal May 2000
Critical phenomena and renormalization-group theory journal October 2002
Theoretical estimates of the critical exponents of the superfluid transition in He 4 by lattice methods journal October 2006
The lightcone bootstrap and the spectrum of the 3d Ising CFT journal March 2017
More analytic bootstrap: nonperturbative effects and fermions journal August 2019
Critical exponents of the N -vector model journal October 1998
Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions journal January 2001
The $\epsilon $-expansion from conformal field theory journal July 2015
Multicritical phenomena in O ( n 1 ) ⊕ O ( n 2 ) -symmetric theories journal February 2003
Third-harmonic exponent in three-dimensional N -vector models journal September 2003
The stability of the O invariant fixed point in three dimensions journal May 1998
Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models journal February 2020
Positivity constraints for anomalous dimensions journal October 1973
Convexity and liberation at large spin journal November 2013
Bounds for OPE coefficients on the Regge trajectory journal October 2017
The analytic bootstrap and AdS superhorizon locality journal December 2013
An Iterative Rank Penalty Method for Nonconvex Quadratically Constrained Quadratic Programs journal January 2019
Harmonic crossover exponents in O ( n ) models with the pseudo- ϵ expansion approach journal February 2005
Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography journal December 2014
The conformal bootstrap at finite temperature journal October 2018
XSEDE: Accelerating Scientific Discovery journal September 2014

Figures / Tables (22)

Table 1(p. 4)table Table 1
Figure 1(p. 5)figure Figure 1
Figure 2(p. 8)figure Figure 2
Table 2(p. 12)table Table 2
Table 3(p. 14)table Table 3
Figure 3(p. 18)figure Figure 3
Figure 4(p. 24)figure Figure 4
Figure 5(p. 25)figure Figure 5
Figure 6(p. 26)figure Figure 6
Figure 7(p. 28)figure Figure 7
Figure 8(p. 30)figure Figure 8
Figure 9(p. 31)figure Figure 9
Figure 10(p. 32)figure Figure 10
Figure 11(p. 33)figure Figure 11
Figure 12(p. 34)figure Figure 12
Table 4(p. 35)table Table 4
Table 5(p. 37)table Table 5
Table 6(p. 37)table Table 6
Table 7(p. 43)table Table 7
Table 8(p. 44)table Table 8
Table 10(p. 45)table Table 10
Table 9(p. 45)table Table 9

Similar Records

Bootstrapping Heisenberg magnets and their cubic instability
Journal Article · 2021 · Physical Review. D. · OSTI ID:1831286
+4 more
The Gross-Neveu-Yukawa archipelago
Journal Article · 2023 · Journal of High Energy Physics (Online) · OSTI ID:2419925
+3 more
Fermion conformal bootstrap in 4d
Journal Article · 2019 · Journal of High Energy Physics (Online) · OSTI ID:1596663
+1 more

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Conformal and W Symmetry
Conformal Field Theory
Global Symmetries