Weizmann lectures on the numerical conformal bootstrap

IF 23.9 1区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Physics Reports Pub Date : 2023-11-03 DOI:10.1016/j.physrep.2023.10.008

Shai M. Chester

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引用次数: 53

Abstract

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 conformal field theory in $d > 2$ spacetime dimensions, we discuss how to compute conformal blocks, formulate the crossing equations as a semi-definite programming problem, solve this problem using SDPB on a personal computer, and interpret the results. We include worked examples for all steps, including bounds for 3d CFTs with $Z_{2}$ or $O (N)$ global symmetries. Each lecture includes a problem set, which culminate in a precise computation of the 3d Ising model critical exponents using the mixed correlator $Z_{2}$ bootstrap. A Mathematica file is included that transforms crossing equations into the proper input form for SDPB.

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Weizmann讲授数值共形自举

这些讲座于2019年春季在魏茨曼研究所举办。它们旨在让学生尽可能有效地熟悉数字引导的细节。在简要回顾了d>；在2个时空维度上，我们讨论了如何计算共形块，将交叉方程公式化为半定规划问题，在个人计算机上使用SDPB解决这个问题，并解释了结果。我们包括了所有步骤的工作示例，包括具有Z2或O（N）全局对称性的三维CFT的边界。每节课都包括一个问题集，最终使用混合相关器Z2 bootstrap精确计算三维伊辛模型临界指数。包括一个Mathematica文件，该文件将交叉方程转换为SDPB的正确输入形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physics Reports 物理-物理：综合

CiteScore

56.10

自引率

0.70%

发文量

102

审稿时长

9.1 weeks

期刊介绍： Physics Reports keeps the active physicist up-to-date on developments in a wide range of topics by publishing timely reviews which are more extensive than just literature surveys but normally less than a full monograph. Each report deals with one specific subject and is generally published in a separate volume. These reviews are specialist in nature but contain enough introductory material to make the main points intelligible to a non-specialist. The reader will not only be able to distinguish important developments and trends in physics but will also find a sufficient number of references to the original literature.