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Navigator function for the conformal bootstrap

Reehorst, Marten and Rychkov, Slava and Simmons-Duffin, David and Sirois, Benoit and Su, Ning and van Rees, Balt (2021) Navigator function for the conformal bootstrap. SciPost Physics, 11 (3). Art. No. 72. ISSN 2542-4653. doi:10.21468/scipostphys.11.3.072.

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Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information “allowed”/“excluded” with a continuous “navigator” function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Rychkov, Slava0000-0002-5847-1011
Simmons-Duffin, David0000-0002-2937-9515
Sirois, Benoit0000-0003-3260-4135
Su, Ning0000-0001-5559-7922
van Rees, Balt0000-0003-0904-5881
Additional Information:© 2021 M. Reehorst et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 15-05-2021; Accepted 08-09-2021; Published 28-09-2021. We thank Tom Hartman for important conversations that sparked this exploration. We thank Walter Landry for discussions and for collaboration on the program approx_objective for computing variations of the objective function. NS thanks Shixin Zhang, Yinchen He for inspiring discussions. NS thanks his parents for support during the COVID-19 pandemic. MR is supported by Mitsubishi Heavy Industries (MHI-ENS Chair). BS is supported by a Fonds de Recherche du Québec – Nature et technologies B1X Master’s scholarship. DSD is supported by Simons Foundation grant #488657 (Simons Collaboration on the Nonperturbative Bootstrap) and a DOE Early Career Award under grant no. DE-SC0019085. BvR is supported by Simons Foundation grant #488659 (Simons Collaboration on the Nonperturbative bootstrap). NS is supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 758903). SR is supported by the Simons Foundation grant 488655 and 733758 (Simons Collaboration on the Nonperturbative Bootstrap), and by Mitsubishi Heavy Industries as an ENS-MHI Chair holder. Some of the computations in this work were performed on the Caltech High Performance Cluster, partially supported by a grant from the Gordon and Betty Moore Foundation. This work also 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. The computations in this paper were partially run on the Symmetry cluster of Perimeter institute and on the Hopper cluster of the École Polytechnique.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Fonds de recherche du Québec - Nature et technologies (FRQNT)UNSPECIFIED
Simons Foundation488657
Department of Energy (DOE)DE-SC0019085
Simons Foundation488659
European Research Council (ERC)758903
Simons Foundation488655
Simons Foundation733758
Mitsubishi Heavy IndustriesUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20211117-173310983
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111920
Deposited By: Tony Diaz
Deposited On:17 Nov 2021 23:22
Last Modified:17 Nov 2021 23:22

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