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.
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.Attached Files
Published - SciPostPhys_11_3_072.pdf
Accepted Version - 2104.09518.pdf
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Additional details
- Eprint ID
- 111920
- Resolver ID
- CaltechAUTHORS:20211117-173310983
- Fonds de recherche du Québec - Nature et technologies (FRQNT)
- 488657
- Simons Foundation
- DE-SC0019085
- Department of Energy (DOE)
- 488659
- Simons Foundation
- 758903
- European Research Council (ERC)
- 488655
- Simons Foundation
- 733758
- Simons Foundation
- Mitsubishi Heavy Industries
- Gordon and Betty Moore Foundation
- PHY-190023
- NSF
- ACI-1548562
- NSF
- Created
-
2021-11-17Created from EPrint's datestamp field
- Updated
-
2021-11-17Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics