Harmonic crossover exponents in O ( n ) models with the pseudo- ϵ expansion approach

326

602

We study the conformal bootstrap for 3D CFTs with O(N ) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N ) singlet and symmetric tensor operators appearing in the φ i × φ j OPE, where φ i is a fundamental of O(N ). Comparing these bounds to previous determinations of critical exponents in the O(N ) vector models, we find strong numerical evidence that the O(N ) vector models saturate the bootstrap constraints at all values of N . We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N ) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N .

Section: Bounds On O(n ) Symmetric Tensorssupporting

confidence: 68%

Bootstrapping the O(N ) vector models

Kos

Poland

Simmons-Duffin

2014

326

602

“…The results for ∆ φ are compared with the recent Monte Carlo studies [86,95] and an earlier study combining Monte Carlo simulations with high temperature expansion calculations [96], while the results for ∆ t are compared with the Monte Carlo study [87]. The latter is also compatible with the earlier pseudo-expansion estimate ∆ t = 1.237( 8) [116].…”

Section: Central Charges and λ φφSsupporting

confidence: 54%

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

Chester

Landry

Liu

et al. 2020

164

217

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.

“…We tabulate this error in appendix A. The green rectangle represents the error bars from Monte Carlo [56] and the pseudo-ǫ expansion approach [57]. Note that our estimate for ∆ t in (3.2) was computed with Λ = 35, so it is more precise than the region pictured here.…”

Section: O(n ) N >mentioning

confidence: 99%

Bootstrapping the O(N) archipelago

Kos

Poland

Simmons-Duffin

et al. 2015

218

377

We study 3d CFTs with an O(N ) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N ) vector φ i and the lowest dimension O(N ) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (∆ φ , ∆ s ) to lie inside small islands. We also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.