A Semidefinite Program Solver for the Conformal Bootstrap

TL;DR

SDPB is an open-source, high-performance semidefinite program solver tailored for the conformal bootstrap, enabling precise bounds on operator dimensions in conformal field theories.

Contribution

The paper introduces SDPB, a specialized, parallelized solver that outperforms existing tools and facilitates advanced conformal bootstrap computations.

Findings

Computed high-precision bounds on 3d Ising CFT operator dimensions

Demonstrated SDPB's superior performance over generic solvers

Enabled new rigorous constraints in conformal bootstrap studies

Abstract

We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an example application, we compute a new rigorous high-precision bound on operator dimensions in the 3d Ising CFT, $\Delta_\sigma=0.518151(6)$, $\Delta_\epsilon=1.41264(6)$.