Related papers: Numerical Methods in the Conformal Bootstrap
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
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…
The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may…
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…
We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible…
We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an implementation of Dantzig's simplex method capable of handling arbitrary precision linear…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
Conformal predictors are an important class of algorithms that allow predictions to be made with a user-defined confidence level. They are able to do this by outputting prediction sets, rather than simple point predictions. The conformal…
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…
This review aims to offer a pedagogical introduction to the analytic conformal bootstrap program via a journey through selected topics. We review analytic methods which include the large spin perturbation theory, Mellin space methods and…
This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these…
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…
We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
The method of extremal flows has presented an alluring alternative approach to numerically solving bootstrap constraints. Here I present the development and adaptation of that approach to a more general class of flows with apparent…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
Conformal Predictors (CP) are wrappers around ML models, providing error guarantees under weak assumptions on the data distribution. They are suitable for a wide range of problems, from classification and regression to anomaly detection.…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…