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  • Letter
  • Open Access

Polyakov blocks for the 1D conformal field theory mixed-correlator bootstrap

Kausik Ghosh1,*, Apratim Kaviraj2,†, and Miguel F. Paulos1,‡

  • 1Laboratoire de Physique Théorique, de l’École Normale Supérieure, PSL University, CNRS, Sorbonne Universités, UPMC University Paris 06, 24 rue Lhomond, 75231 Paris Cedex 05, France
  • 2Deutsches Elektronen Synchroton DESY, Notkestrasse 85, 22603 Hamburg, Germany

  • *kau.rock91@gmail.com
  • †apratim.kaviraj@desy.de
  • ‡miguel.paulos@ens.fr
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Phys. Rev. D 109, L061703 – Published 29 March, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L061703

Abstract

We introduce manifestly crossing-symmetric expansions for arbitrary systems of 1D CFT correlators. These expansions are given in terms of certain Polyakov blocks which we define and show how to compute efficiently. Equality of operator product expansion and Polyakov block expansions leads to sets of sum rules that any mixed correlator system must satisfy. The sum rules are diagonalized by correlators in tensor product theories of generalized free fields. We show that it is possible to do a change of a basis that diagonalizes instead mixed correlator systems involving elementary and composite operators in a single field theory. As an application, we find the first nontrivial examples of optimal bounds, saturated by the mixed correlator system ϕ,ϕ2 in the theory of a single generalized free field.

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Outline

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Phys. Rev. D 109, L061703– Published 29 March, 2024
  • Received 29 December 2023
  • Accepted 1 March 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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