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Charting the space of 3D CFTs with a continuous global symmetry

  • Anatoly Dymarsky
  • Joao Penedones
  • Emilio TrevisaniEmail author
  • Alessandro Vichi
Open Access
Regular Article - Theoretical Physics
  • 28 Downloads

Abstract

We study correlation functions of a conserved spin-1 current Jμ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point functions \( \left\langle {J}_{\mu }{J}_{\nu }{\mathcal{O}}_{\Delta, \ell}\right\rangle \) and the four point function 〈JμJνJρJσ〉 and identify the minimal set of independent crossing symmetry conditions. We obtain a recurrence relation for conformal blocks for generic spin-1 operators in three dimensions. In the process, we improve several technical points, facilitating the use of recurrence relations. By applying the machinery of the numerical conformal bootstrap we obtain universal bounds on the dimensions of certain light operators as well as the central charge. Highlights of our results include numerical evidence for the conformal collider bound and new constraints on the parameters of the critical O(2) model. The results obtained in this work apply to any unitary, three dimensional CFT.

Keywords

Conformal Field Theory Global Symmetries Field Theories in Higher Dimensions 

Notes

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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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of KentuckyLexingtonU.S.A.
  2. 2.Skolkovo Institute of Science and Technology, Skolkovo Innovation CenterMoscowRussia
  3. 3.Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  4. 4.Centro de Fisica do PortoUniversidade do PortoPortoPortugal
  5. 5.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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