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The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices

Authors
  • Mazáč, Dalimil1, 2
  • Paulos, Miguel F.3
  • 1 Stony Brook University, C.N. Yang Institute for Theoretical Physics, Stony Brook, NY, 11794, U.S.A. , Stony Brook (United States)
  • 2 Stony Brook University, Simons Center for Geometry and Physics, Stony Brook, NY, 11794, U.S.A. , Stony Brook (United States)
  • 3 Sorbonne Universités, UPMC University Paris 06, Laboratoire de Physique Théorique de l’ École Normale Supérieure PSL University, CNRS, 24 rue Lhomond, Paris Cedex 05, 75231, France , Paris Cedex 05 (France)
Type
Published Article
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Publication Date
Feb 25, 2019
Volume
2019
Issue
2
Identifiers
DOI: 10.1007/JHEP02(2019)162
Source
Springer Nature
Keywords
License
Yellow

Abstract

We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in two regimes. The first corresponds to functionals that annihilate the generalized free fermion spectrum. In this case, we analytically find both OPE and gap maximization functionals proving the extremality of the generalized free fermion solution to crossing. Secondly, we consider a scaling limit where all conformal dimensions become large, equivalent to the large AdS radius limit of gapped theories in AdS2. In this regime we demonstrate analytically that optimal bounds on OPE coefficients lead to extremal solutions to crossing arising from integrable field theories placed in large AdS2. In the process, we uncover a close connection between asymptotic extremal functionals and S-matrices of integrable field theories in flat space and explain how 2D S-matrix bootstrap results can be derived from the 1D conformal bootstrap equations. These points illustrate that our formalism is capable of capturing non-trivial solutions of CFT crossing.

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