JuliBootS: a hands-on guide to the conformal bootstrap
Miguel F. Paulos
TL;DR
JuliBootS provides an open-source, Julia-based framework for numerical conformal bootstrap computations by casting crossing symmetry into linear programming and solving with a Dantzig-style simplex method. The package delivers a rational representation of conformal blocks, a convolution framework to incorporate external dimensions, and a modular solver architecture capable of handling discrete and continuous spectra, including global symmetries. It demonstrates practical bootstrap analyses, including bounds on operator dimensions, OPE coefficient maximization, spectrum filtering, and parallel scans, highlighting both methodological flexibility and computational efficiency. Overall, the work lowers the barrier to performing bootstrap experiments and furnishes a platform for future improvements in precision, coverage, and performance.
Abstract
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 programming problems with continuous search spaces. Current supported features include conformal dimension bounds, OPE bounds, and bootstrap with or without global symmetries. The code is trivially parallelizable on one or multiple machines. We exemplify usage extensively with several real-world applications. In passing we give a pedagogical introduction to the numerical bootstrap methods.