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Journal of High Energy Physics

, 2019:201 | Cite as

The large charge limit of scalar field theories, and the Wilson-Fisher fixed point at 𝜖 = 0

  • G. Arias-Tamargo
  • D. Rodriguez-GomezEmail author
  • J.G. Russo
Open Access
Regular Article - Theoretical Physics

Abstract

We study the sector of large charge operators ϕn (ϕ being the complexified scalar field) in the O(2) Wilson-Fisher fixed point in 4−E dimensions that emerges when the coupling takes the critical value g ∼ 𝜖. We show that, in the limit g → 0, when the theory naively approaches the gaussian fixed point, the sector of operators with n → ∞ at fixed g n2≡ λ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator ϕn by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional O(2)-symmetric theory with (\( \overline{\phi} \)ϕ)3 potential.

Keywords

Conformal Field Theory Effective Field Theories Renormalization Group 

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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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • G. Arias-Tamargo
    • 1
    • 2
  • D. Rodriguez-Gomez
    • 1
    • 2
    Email author
  • J.G. Russo
    • 3
    • 4
  1. 1.Department of PhysicsUniversidad de OviedoOviedoSpain
  2. 2.Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)OviedoSpain
  3. 3.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain
  4. 4.Departament de Física Cuántica i Astrofísica and Institut de Cìencies del CosmosUniversitat de BarcelonaBarcelonaSpain

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