SDPB is an open-source, arbitrary-precision, parallelized semidefinite program solver, designed for the conformal bootstrap. It solves the following problem:
Let $S^{m\times m}[x]$ be the space of symmetric $m\times m$ matrices whose entries are polynomials in $x$.
Here, $M\succeq 0$ means "M is positive semidefinite."
For more information, see A Semidefinite Program Solver for the Conformal Bootstrap and the manual.
Authors: David Simmons-Duffin (dsd@caltech.edu), Walter Landry (wlandry@caltech.edu), Vasiliy Dommes (vasdommes@gmail.com)
The easiest way to run SDPB on a Windows or Mac machine is to follow the Docker instructions. For Linux and HPC centers, the Singularity instructions will probably work better. If you want to build it yourself, there are detailed instructions in Install.md.
Usage instructions are detailed in Usage.md.
Two python wrappers for SDPB are available:
An unofficial Haskell wrapper is available:
If you use SDPB in work that results in publication, consider citing
Depending on how SDPB is used, the following other sources might be relevant:
The first use of semidefinite programming in the bootstrap:
The generalization of semidefinite programming methods to arbitrary spacetime dimension:
The generalization of semidefinite programming methods to arbitrary systems of correlation functions:
Derivation of linear and quadratic variations of the objective function, used in approx_objective
:
Spectrum extraction was originally written for use in:
An explanation of how it works appears in:
Versions 2 and 3 of SDPB were made possible by support from the Simons Collaboration on the Nonperturbative Bootstrap.
The design of SDPB was partially based on the solvers SDPA and SDPA-GMP, which were essential sources of inspiration and examples.
Thanks to Filip Kos, David Poland, and Alessandro Vichi for collaboration in developing semidefinite programming methods for the conformal bootstrap and assistance testing SDPB.
Thanks to Amir Ali Ahmadi, Hande Benson, Pablo Parrilo, and Robert Vanderbei for advice and discussions about semidefinite programming.
Thanks also to Noah Stein, who first suggested the idea of semidefinite programming to me in this Math Overflow question.
Here is a list of papers citing SDPB.