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 everywhere well-defined, 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.

60 pages, 22 figures. v2: minor changes and fixes, added subsection 3.1 on differentiability

References in corpus (3)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bounds on 4D Conformal and Superconformal Field Theories

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