相关论文: An Automated Generation of Bootstrap Equations for…

Given a conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three-dimensional real projective space. We check the rapid…

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…

These lectures were given at the Weizmann Institute in the spring of 2019. They are intended to familiarize students with the nuts and bolts of the numerical bootstrap as efficiently as possible. After a brief review of the basics of…

The single-correlator conformal bootstrap is solved numerically for several values of dimension 4>d>2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained…

We study the tricritical Ising universality class using conformal bootstrap techniques. By studying bootstrap constraints originating from multiple correlators on the CFT data of multiple OPEs, we are able to determine the scaling dimension…

We introduce autoboot, a Mathematica program which automatically generates mixed-correlator bootstrap equations of an arbitrary number of scalar external operators, given the global symmetry group and the representations of the operators.…

The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance of…

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal…

The bootstrap is a foundational tool in statistical inference, but its classical implementation relies on Monte Carlo resampling, introducing approximation error and incurring high computational cost -- especially for large datasets and…

As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by physical systems, such as the liquid-vapor transition. Its…

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…

The $d=2$ critical Ising model is described by an exactly solvable Conformal Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple system at strong coupling outside of even dimensions. Using novel numerical and…

We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and…

We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…

We construct a conformal map from $\mathbb{R}^3$ to a three-dimensional spheriod, which includes $\mathbb{S}^3$, a double-cover of the 3-ball, and $\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the critical…

We use the conformal bootstrap program to derive necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g. $\mathbb{Z}_n$) to continuous symmetry (e.g. $U(1)$) under the renormalization group flow. In three…

We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal…

We introduce PPBoot: a bootstrap-based method for prediction-powered inference. PPBoot is applicable to arbitrary estimation problems and is very simple to implement, essentially only requiring one application of the bootstrap. Through a…

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators $\sigma$ and $\epsilon$, and the stress tensor $T_{\mu\nu}$. We…

Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly…