- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Singularities in the RG flow

Antal Jakovác*

  • *Contact author: jakovac.antal@wigner.hun-ren.hu
PDF

Phys. Rev. D 114, 045001 – Published 3 August, 2026

DOI: https://doi.org/10.1103/3wv1-fbg9

Abstract

In this work, we show examples when a perturbatively irrelevant operator becomes relevant in the infrared because of the presence of an IR singularity (IR Landau pole). An example of this behavior is the four-fermion interaction that allows the formation of bound states. The reason for the appearance of the IR Landau pole is not the singular loop as in the purely perturbative case, but the infinite number of modes appearing in the renormalization group flow.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (26)

  1. Sandor Nagy, Lectures on renormalization and asymptotic safety, Ann. Phys. (Amsterdam) 350, 310 (2014).
  2. H. Georgi, Effective field theory, Annu. Rev. Nucl. Part. Sci. 43, 209 (1993).
  3. D. B. Kaplan, Five lectures on effective field theory, arXiv:nucl-th/0510023.
  4. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, New York, 1995).
  5. T. P. Cheng and L. F. Li, Gauge Theory of Elementary Particle Physics (Oxford University Press, New York, 1984).

  6. The number is typically quoted as 18 for the minimal model, extending to 26 if one includes CP-violating phases and right-handed neutrinos.

  7. G. C. Branco, L. Lavoura, and J. P. Silva, CP Violation (Oxford University Press, New York, 1999).
  8. S. Antusch, J. Kersten, M. Lindner, and M. Ratz, Running neutrino mass parameters in see-saw scenarios, Phys. Lett. B 538, 87 (2002).
  9. Edward W. Kolb and Michael S. Turner, The Early Universe, Frontiers in Physics (Westview Press, Boulder, CO, 1990).
  10. Hans A. Bethe and Edwin E. Salpeter, A relativistic equation for bound-state problems, Phys. Rev. 84, 1232 (1951).
  11. Christof Wetterich, Exact evolution equation for the effective average action, Phys. Lett. B 301, 90 (1993).
  12. Jürgen Berges, Nikolaos Tetradis, and Christof Wetterich, Non-perturbative renormalization flow in quantum field theory and statistical physics, Phys. Rep. 363, 223 (2002).
  13. János Polonyi, Lectures on the functional renormalization group method, Central Eur. J. Phys. 1, 1 (2003).
  14. Jean Alexandre, Vincenzo Branchina, and Janos Polonyi, Global renormalization group, Phys. Rev. D 58, 016002 (1998).
  15. J. Polchinski, Renormalization and effective Lagrangians, Nucl. Phys. B231, 269 (1984).
  16. Holger Gies, Renormalization flow of QED, Phys. Rev. D 70, 085018 (2004).
  17. Holger Gies, Introduction to the functional RG and applications to gauge theories, in Renormalization Group and Effective Field Theory Approaches to Many-Body Systems, Vol. 852 of Lecture Notes in Physics, edited by Achim Schwenk and Janos Polonyi (Springer, New York, 2012). See section on gauge and QED applications.
  18. Holger Gies and Christof Wetterich, Renormalization flow of bound states, Phys. Rev. D 65, 065001 (2002).
  19. Jürgen Berges, D.-U. Jungnickel, and Christof Wetterich, Two-flavor chiral phase transition from nonperturbative flow equations, Phys. Rev. D 59, 034010 (1999).
  20. Antal Jakovác and András Patkós, Bound states in functional renormalization group, Int. J. Mod. Phys. A 34, 1950154 (2019).
  21. Gribov-90 Memorial Volume: Field Theory, Symmetry, and Related Topics: Proceedings of the Memorial Workshop Devoted to the 90th Birthday of V N Gribov, edited by Y. Dokshitzer, P. Lévai, A. Lukács, and J. Nyíri (World Scientific, 2021).
  22. Gergely Fejős, Masoud Kobayashi, Chandan Chatterjee, and Muneto Nitta, Vortex confinement transitions in the modified goldstone model, Phys. Rev. Res. 2, 013081 (2020).
  23. Jens Braun, Marc Leonhardt, and Martin Pospiech, Fierz-complete NJL model study: Fixed points and phase structure at finite temperature and density, Phys. Rev. D 96, 076003 (2017).
  24. Jens Braun, Marc Leonhardt, and Martin Pospiech, Fierz-complete NJL model study. II. Toward the fixed-point and phase structure of hot and dense two-flavor QCD, Phys. Rev. D 97, 076010 (2018).
  25. Jens Braun, Marc Leonhardt, and Martin Pospiech, Fierz-complete NJL model study. III. Emergence from quark-gluon dynamics, Phys. Rev. D 101, 036004 (2020).
  26. Nobuhiro Nakanishi, A general survey of the theory of the Bethe–Salpeter equation, Prog. Theor. Phys. Suppl., 43 1 (1969).

Outline

Information

Phys. Rev. D 114, 045001– Published 3 August, 2026
  • Received 9 March 2026
  • Accepted 29 May 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation