Exact summation of leading infrared logarithms in 2D effective field theories

  • Jonas Linzen
  • Maxim V. PolyakovEmail author
  • Kirill M. Semenov-Tian-Shansky
  • Nika S. Sokolova
Open Access
Regular Article - Theoretical Physics


A method of exact all-order summation of leading infrared logarithms in two dimensional massless Φ4-type non-renormalizable effective field theories (EFTs) is developed. The method is applied to the O(N)-symmetric EFT, which is a two-dimensional sibling of the four dimensional O(N + 1)/O(N) sigma-model. For the first time the exact all-order summation of the (E2ln(1/E))n contributions (chiral logarithms) for the 2 → 2 scattering amplitudes is performed in closed analytical form. The cases when the resulting amplitudes turn to be meromorphic functions with an infinite number of poles (Landau poles) are identified. This provides the first explicit example of quasi-renormalizable field theories.


Effective Field Theories Sigma Models Field Theories in Lower Dimensions Renormalization Group 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Jonas Linzen
    • 1
  • Maxim V. Polyakov
    • 1
    • 2
    Email author
  • Kirill M. Semenov-Tian-Shansky
    • 2
    • 3
  • Nika S. Sokolova
    • 2
    • 4
  1. 1.Institute of Theoretical Physics II, Faculty of Physics and AstronomyRuhr University BochumBochumGermany
  2. 2.National Research Centre “Kurchatov Institute”: Petersburg Nuclear Physics InstituteGatchinaRussia
  3. 3.Saint Petersburg National Research Academic University of the Russian Academy of SciencesSt. PetersburgRussia
  4. 4.Faculty of PhysicsSt. Petersburg State UniversityPeterhofRussia

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