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 time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coecients in the Ising and O(N) models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

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保形引导程序：理论，数值技术和应用

保形场论是描述尺度不变临界点的引人入胜的普遍物理学，早已为人所知。他们描述了流体，磁体和许多其他材料中的连续相变，同时又是我们对量子场论的现代理解的核心。几十年来，一直梦想着使用对称性和其他一致性条件无扰动地研究这些复杂的强耦合理论。这个称为共形引导程序的想法在两个方面取得了一些成功，但是直到最近十年才在三个，四个和其他感兴趣的方面得到了充分的实现。这种复兴之所以成为可能，不仅是因为在了解如何建立自举方程式方面取得了重大的分析进展，而且还发展了用于寻找或约束其解的数值技术。这些发展带来了许多突破性的结果，包括在三个维度的Ising和O（N）模型中对关键指数和相关函数系数的世界纪录确定。本文将回顾引导程序新手的这些激动人心的发展，介绍共形场理论和共形块理论，描述基于凸优化的引导程序数值技术，并详细概述它们在固定点和三个方面的应用。没有或只有极小的超对称的四个维度。这些发展带来了许多突破性的结果，包括在三个维度的Ising和O（N）模型中对关键指数和相关函数系数的世界纪录确定。本文将回顾引导程序新手的这些激动人心的发展，介绍共形场理论和共形块理论，描述基于凸优化的引导程序数值技术，并详细概述它们在固定点和三个方面的应用。没有或只有极小的超对称的四个维度。这些发展带来了许多突破性的结果，包括在三个维度的Ising和O（N）模型中对关键指数和相关函数系数的世界纪录确定。本文将回顾引导程序新手的这些激动人心的发展，介绍共形场理论和共形块理论，描述基于凸优化的引导程序数值技术，并详细概述它们在固定点和三个方面的应用。没有或只有极小的超对称的四个维度。