Navigator function for the conformal bootstrap
Marten Reehorst, Slava Rychkov, David Simmons-Duffin, Benoit Sirois, Ning Su, Balt van Rees
SciPost Phys. 11, 072 (2021) · published 28 September 2021
- doi: 10.21468/SciPostPhys.11.3.072
- Submissions/Reports
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.
Cited by 28
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Marten Reehorst,
- 1 2 Slava Rychkov,
- 3 David Simmons-Duffin,
- 1 2 Benoit Sirois,
- 4 Ning Su,
- 5 Balt van Rees
- 1 Institut des Hautes Études Scientifiques [IHÉS]
- 2 École Normale Supérieure [ENS]
- 3 Walter Burke Institute for Theoretical Physics
- 4 Università di Pisa / University of Pisa [UniPi]
- 5 Centre de Physique Théorique / Center of Theoretical Physics [CPHT]
- European Research Council [ERC]
- Fonds de Recherche du Québec - Nature et Technologies (through Organization: Fonds de Recherche du Québec – Nature et technologies [FRQNT])
- Gordon and Betty Moore Foundation
- Mitsubishi International Corporation (through Organization: 三菱重工業株式会社 / Mitsubishi Heavy Industries (Japan) [MHI])
- National Science Foundation [NSF]
- Simons Foundation
- United States Department of Energy [DOE]