Carving out OPE space and precise O(2) model critical exponents

Creators: Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Sun, Ning; Vichi, Alessandro

Abstract

We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.

Additional Information

© 2020 The Author(s). 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. Article funded by SCOAP3. Received: February 25, 2020. Revised: April 28, 2020. Accepted: May 18, 2020. Published: June 23, 2020. We thank David Meltzer, Slava Rychkov and Ettore Vicari for discussions. AV and SMC thank Filip Kos for collaboration at an early stage of this project. NS thanks Junchen Rong for discussions. DSD and JL thank Brad Filippone for discussions on the Lambda Point Experiment and for his excellent demonstration of the super fluid ⁴He phase transition, performed annually (on Earth) for Caltech undergrads in Physics 2c/12c. WL, JL, and DSD are supported by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap). DSD and JL are also supported by a Sloan Research Fellowship, and a DOE Early Career Award under grant no. DE-SC0019085. DP is supported by Simons Foundation grant 488651 (Simons Collaboration on the Nonperturbative Bootstrap) and DOE grant no. DE-SC0020318. NS and AV are supported by the European Research Council (ERC) Starting Grant no. 758903. AV is also supported by the Swiss National Science Foundation (SNSF) under grant no. PP00P2-163670. SMC is supported by a Zuckerman STEM Leadership Fellowship. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) Comet Cluster at the San Diego Supercomputing Center (SDSC) through allocation PHY190023, which is supported by National Science Foundation grant number ACI-1548562. This work also used the EPFL SCITAS cluster, which is supported by the SNSF grant PP00P2-163670, the Caltech High Performance Cluster, partially supported by a grant from the Gordon and Betty Moore Foundation, and the Grace computing cluster, supported by the facilities and staff of the Yale University Faculty of Sciences High Performance Computing Center. Code availability: All code used in this work is available online. This includes The semidefinite program solver SDPB: https://github.com/davidsd/sdpb Code for generating tables of scalar conformal blocks: https://gitlab.com/bootstrapcollaboration/scalar blocks A Mathematica framework for bootstrap calculations, including implementations of the cutting surface and Delaunay triangulation algorithms described in section 3: https://gitlab.com/bootstrapcollaboration/simpleboot. A Haskell framework for concurrent computations on an HPC cluster: https://github.com/davidsd/hyperion Haskell libraries for bootstrap computations, including implementations of the cutting surface and Delaunay triangulation algorithms described in section 3: https://gitlab.com/davidsd/sdpb-haskell https://gitlab.com/davidsd/hyperion-bootstrap https://gitlab.com/davidsd/hyperion-projects A Haskell library and standalone executable for solving quadratically constrained problems by a combination of semidefinite relaxation and other heuristics https://gitlab.com/davidsd/quadratic-net/

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