A semidefinite program solver for the conformal bootstrap

Creators: Simmons-Duffin, David

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, Δ_σ = 0.518151(6), Δ_ϵ = 1.41264(6).

Additional Information

© 2015 The Author(s). Received: March 21, 2015 Accepted: June 7, 2015 Published: June 25, 2015 I am grateful to Chris Beem, Luca Iliesiu, Silviu Pufu, Slava Rychkov, Balt van Rees, and Ran Yacoby for related discussions, and especially Filip Kos, David Poland, and Alessandro Vichi for discussions, collaboration, assistance testing SDPB, and comments on the draft. Thanks also to Slava Rychkov for comments on the draft. Thanks to Amir Ali Ahmadi, Hande Benson, Pablo Parrilo, and Robert Vanderbei for advice on semidefinite programming and numerical optimization. I am supported by DOE grant number DE-SC0009988 and a William D. Loughlin Membership at the Institute for Advanced Study. The computations in this paper were run on the Hyperion computing cluster supported by the School of Natural Sciences Computing Staff at the Institute for Advanced Study. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Published - 10.1007_2FJHEP06_2015_174.pdf

Submitted - 1502.02033.pdf

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