Related papers: The Effective Bootstrap
We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in…
The bootstrap is a versatile inference method that has proven powerful in many statistical problems. However, when applied to modern large-scale models, it could face substantial computation demand from repeated data resampling and model…
$O(n) \times O(m)$ symmetric Landau-Ginzburg models in $d=3$ dimension possess a rich structure of the renormalization group and its understanding offers a theoretical prediction of the phase diagram in frustrated spin models with…
The consistency of a bootstrap or resampling scheme is classically validated by weak convergence of conditional laws. However, when working with stochastic processes in the space of bounded functions and their weak convergence in the…
We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of…
In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access…
We explore how matrix bootstrap techniques can be used to constrain matrix and tensor models at finite $N$, where $N$ is the dimension of the matrix/tensor, taking a Gaussian model with a quartic interaction as example. For matrix models,…
Conformal field theories play a central role in theoretical physics with many applications ranging from condensed matter to string theory. The conformal bootstrap studies conformal field theories using mathematical consistency conditions…
We clarify the relationships between different approaches to the conformal bootstrap. A central role is played by the so-called extremal functionals. They are linear functionals acting on the crossing equation which are directly responsible…
We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can…
Under the assumption that degenerate fields exist, diagonal CFTs such as Liouville theory can be solved analytically using the conformal bootstrap method. Here we generalize this approach to non-diagonal CFTs, i.e. CFTs whose primary fields…
We propose a new class of multiplier bootstraps for count functionals, ranging from a fast, approximate linear bootstrap tailored to sparse, massive graphs to a quadratic bootstrap procedure that offers refined accuracy for smaller, denser…
We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on $S^1\times \mathbb{R}^{d-1}$. The proposed approach does not rely on positivity constraints and does not…
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…
In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As…
Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…
The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations…
We present a systematic exploration of conformal field theories (CFTs) constrained by duality-inspired fusion rules using the conformal bootstrap. We classify the operator spectrum into three sectors: $[\sigma]$, $[\epsilon]$, and $[1]$.…
The soft bootstrap is an on-shell method to constrain the landscape of effective field theories (EFTs) of massless particles via the consistency of the low-energy S-matrix. Given assumptions on the on-shell data (particle spectra, linear…
Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known…