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Title: Navigator function for the conformal bootstrap

Abstract

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.

Authors:
 [1];  [2];  [3];  [2];  [4];  [5]
+ Show Author Affiliations
  1. Institut des Hautes Études Scientifiques
  2. Institut des Hautes Études Scientifiques, École Normale Supérieure
  3. Walter Burke Institute for Theoretical Physics
  4. University of Pisa
  5. Center of Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States); Institut des Hautes Études Scientifiques, Bures-sur-Yvette (France)
Sponsoring Org.:
USDOE; Simons Foundation; European Research Council (ERC); Mitsubishi Heavy Industries; National Science Foundation (NSF)
OSTI Identifier:
1822484
Alternate Identifier(s):
OSTI ID: 1852805
Grant/Contract Number:  
SC0019085; 488657; 488659; 758903; 488655; 733758; PHY190023; ACI-1548562
Resource Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 11 Journal Issue: 3; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Reehorst, Marten, Rychkov, Slava, Simmons-Duffin, David, Sirois, Benoit, Su, Ning, and van Rees, Balt. Navigator function for the conformal bootstrap. Netherlands: N. p., 2021. Web. doi:10.21468/SciPostPhys.11.3.072.
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Reehorst, Marten, Rychkov, Slava, Simmons-Duffin, David, Sirois, Benoit, Su, Ning, & van Rees, Balt. Navigator function for the conformal bootstrap. Netherlands. https://doi.org/10.21468/SciPostPhys.11.3.072
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Reehorst, Marten, Rychkov, Slava, Simmons-Duffin, David, Sirois, Benoit, Su, Ning, and van Rees, Balt. Tue . "Navigator function for the conformal bootstrap". Netherlands. https://doi.org/10.21468/SciPostPhys.11.3.072.
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@article{osti_1822484,
title = {Navigator function for the conformal bootstrap},
author = {Reehorst, Marten and Rychkov, Slava and Simmons-Duffin, David and Sirois, Benoit and Su, Ning and van Rees, Balt},
abstractNote = {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.},
doi = {10.21468/SciPostPhys.11.3.072},
journal = {SciPost Physics},
number = 3,
volume = 11,
place = {Netherlands},
year = {Tue Sep 28 00:00:00 EDT 2021},
month = {Tue Sep 28 00:00:00 EDT 2021}
}
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Journal Article:
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https://doi.org/10.21468/SciPostPhys.11.3.072
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