Extremal bootstrapping: go with the flow

  • Sheer El-Showk
  • Miguel F. Paulos
Open Access
Regular Article - Theoretical Physics


The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may be used to flow continuously along the boundaries of parameter space. Along the flow there is generically no further need for optimization, which dramatically reduces computational requirements, bringing calculations from the realm of computing clusters to laptops. Conceptually, extremality sheds light on possible ways to bootstrap without positivity, extending the method to non-unitary theories, and implies that theories saturating bounds, and especially those sitting at kinks, have unusually sparse spectra. We discuss several applications, including the first high-precision bootstrap of a non-unitary CFT.


Conformal and W Symmetry Conformal Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Theoretical Physics Department, CERNGenevaSwitzerland

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