Weizmann lectures on the numerical conformal bootstrap

Shai M. Chester

doi:10.1016/j.physrep.2023.10.008

Weizmann lectures on the numerical conformal bootstrap

Shai M. Chester

Department of Particle Physics and Astrophysics

Research output: Contribution to journal › Review article › peer-review

9 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	1-44
Number of pages	44
Journal	Physics Reports
Volume	1045
Early online date	3 Nov 2023
DOIs	https://doi.org/10.1016/j.physrep.2023.10.008
Publication status	Published - 19 Dec 2023

Funding

We thank Ofer Aharony for carefully reading through the manuscript, and him and Petr Kravchuk, Walter Landry, Silviu Pufu, David Simmons-Duffin, Ryan Thorngren and Emilio Trevisani for useful discussions. Special thanks to Alessandro Vichi for the original wrapper code that Bootstrap.m is based on. We also thank all the members of the Weizmann 2019 Bootstrap class for pointing out many errors and typos, and especially Ohad Mamroud, Rohit Reghupathy, and Erez Urbach for troubleshooting the problem sets. SMC is supported by the Zuckerman STEM Leadership Fellowship, Israel.

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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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 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.",

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AB - 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.

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Weizmann lectures on the numerical conformal bootstrap

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