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

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.

Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories

“…In the following we will show that the critical behavior along the phase transition line of two-flavor SO (3) I: Some estimates of the universal critical exponents for the 3D XY universality class, obtained from the analysis of high-temperature expansions supplemented by MC simulations [35], from MC simulations [36] and the conformalbootstrap approach [37]. See Ref.…”

Distributions in CFT II. Minkowski Space

“…The latter requirement is somewhat analogous to having the Wightman cluster property (2.4) to be satisfied only for spacelike a. 18 Note that the Minkowski operators can be mapped to Euclidean operators. In particular any SO(1, d − 1) irrep can be mapped to an SO(d) irrep.…”

“…QFTs invariant under the action of conformal group, which are nowadays studied via the conformal bootstrap. This axiomatic approach led to precise determinations of many experimentally measurable quantities, such as the critical exponents of the 3d Ising [11][12][13][14][15], O(N ) [15][16][17][18][19] and other critical points (see review [20]). 2 The numerical conformal bootstrap relies on the "Euclidean CFT axioms", 3 which specify properties of correlation functions in any unitary CFT in R d via a set of simple and commonly accepted rules, such as the unitarity bounds on primary operator dimensions, conformally invariant and convergent Operator Product Expansion (OPE), and reality constraints on OPE coefficients.…”

Mixed Correlator Dispersive CFT Sum Rules

“…The success of the modern conformal bootstrap stands upon the pillars of high precision numerical methods [1,2], and deeper understanding of the analytic structure of the bootstrap equations (see [3,4] and references therein). Numerical methods have led to high precision measurements of critical exponents of conformal field theories (CFTs) such as the 3D Ising [5][6][7][8] and the O(N ) models [9][10][11], while analytical methods have proven essential to the study of quantum gravity in Anti-de Sitter (AdS) spacetime [12][13][14][15][16][17] and perturbative CFTs [18,19].…”

“…11 in Mellin-space for convenience: By evaluating the Mellin amplitude (correlator) in the s-channel collinear limit, we restrict ourselves to the leading double-twist n = 0 sector. In general, for the collinear B k;t|mn functionals, we have for arbitrary subtraction schemes…”