A functional approach to the numerical conformal bootstrap

Abstract We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of comp...

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Bibliographic Details
Main Authors: Miguel F. Paulos, Bernardo Zan
Format: Article
Language:English
Published: SpringerOpen 2020-09-01
Series:Journal of High Energy Physics
Subjects:
Online Access:http://link.springer.com/article/10.1007/JHEP09(2020)006
Description
Summary:Abstract We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in opposition to hundreds of components in the usual approach. We explain how this is a consequence of the functional basis correctly capturing the asymptotics of bound-saturating extremal solutions to crossing. We discuss how these methods can and should be implemented in higher dimensional applications.
ISSN:1029-8479