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Weizmann lectures on the numerical conformal bootstrap
Physics Reports ( IF 30.0 ) Pub Date : 2023-11-03 , DOI: 10.1016/j.physrep.2023.10.008
Shai M. Chester

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 Z2 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 Z2 bootstrap. A Mathematica file is included that transforms crossing equations into the proper input form for SDPB.



中文翻译:

魏茨曼关于数值共形自举法的讲座

这些讲座于 2019 年春季在魏茨曼研究所举行。旨在让学生尽可能高效地熟悉数值引导法的具体细节。在简要回顾了共形场论的基础知识之后d>2时空维度,我们讨论如何计算共形块,将交叉方程表示为半定规划问题,在个人计算机上使用SDPB解决该问题,并解释结果。我们包含所有步骤的工作示例,包括 3d CFT 的边界Z2或者全局对称性。每个讲座都包含一个问题集,最终使用混合相关器精确计算 3d Ising 模型关键指数Z2引导程序。其中包含一个Mathematica文件,可将交叉方程转换为SDPB的正确输入形式。

更新日期:2023-11-05
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