A Semidefinite Program Solver for the Conformal Bootstrap

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, ${\Delta }_{\sigma }=0.518151(6)$, ${\Delta }_{\epsilon }=1.41264(6)$.

34 pages, 3 figures, and 3500 lines of C++

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• The Epsilon-Expansion from Conformal Field Theory
• Bootstrapping Pure Quantum Gravity in AdS3
• The interface tension in the improved Blume-Capel model