Carving out OPE space and precise O(2) model critical exponents
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Springer
Received: February Revised: April Accepted: May Published: June
25, 28, 18, 23,
2020 2020 2020 2020
Shai M. Chester,a Walter Landry,1,b Junyu Liu,b,c David Poland,b,d David Simmons-Duffin,b Ning Sue and Alessandro Vichie,f a
Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel b Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, CA 91125, U.S.A. c Institute for Quantum Information and Matter, Caltech, Pasadena, CA 91125, U.S.A. d Department of Physics, Yale University, New Haven, CT 06520, U.S.A. e ´ Institute of Physics, Ecole Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland f Department of Physics, University of Pisa, I-56127 Pisa, Italy
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: 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. Keywords: Conformal and W Symmetry, Conformal Field Theory, Global Symmetries ArXiv ePrint: 1912.03324 1
Simons Collaboration on the Nonperturbative Bootstrap.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)142
JHEP06(2020)142
Carving out OPE space and precise O(2) model critical exponents
Contents 1 1 2 3 4 4 6
2 The O(2) model 2.1 Crossing equations 2.2 Assumptions about the spectrum
7 7 9
3 Methods 3.1 Numerical bootstrap bounds 3.2 Positivity conditions involving the external scalars s, φ, t 3.3 An algorithm for scanning over OPE coefficients 3.4 Finding a point [λn+1 ] 3.4.1 Implementation in Mathematica 3.4.2 Minimizing Qn 3.4.3 Semidefinite relaxation and rank minimization 3.4.4 Choosing [λn+1 ] 3.4.5 Bounding ellipsoids 3.5 Hot-starting 3.6 Primal/dual jumps 3.7 Delaunay triangulation in dimension space
12 12 12 14 15 17 17 18 20 20 21 22 25
4 Results 4.1 Dimension bounds without OPE scans 4.2 Dimension bounds with OPE scans 4.3 Central charges and λφφs 4.4 Estimates from the extremal functional method
27 27 27 30 32
A Code availability
34
B Software setup and parameters
34
C Tensor structures
36
D Crossing vectors
37
E Computed points
41
–i–
JHEP06(2020)142
1 Introduction 1.1 Large-scale bootstrap problems 1.2 Experimental and theoretical approaches to the 3d O(2) model 1.2.1 The λ-point experime
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