- Physical Review Journals
All JournalsPhysics Magazine

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

Scattering in the dual regime of Yang-Baxter deformed O(2N) sigma models

Alexey Bychkov1,2,3 and Boris Nekrasov1

PDF

Phys. Rev. D 113, 066007 – Published 11 March, 2026

DOI: https://doi.org/10.1103/rx84-q4sv

Abstract

We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed O(2N) sigma models, which is a new one-parametric deformation of the O(2N) model. It can be obtained from the conventional YB deformed O(2N+2) sigma model by freezing two isometries. The scattering matrix in the nondeformed O(n) model is known to coincide with the rational son-invariant R-matrix. For n=2N this rational solution allows for two trigonometric deformations: the usual DN(1) and the twisted DN(2). The usual one is known to coincide with the scattering matrix of the conventional YB-O(2N) model. A natural question to ask is what sigma model corresponds to the twisted solution. In this work we claim that it is precisely our dual regime of YB-O(2N). We find the corresponding unitarizing function FN(θ) explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe ansatz technique.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (22)

  1. Murray Gell-Mann and M. Levy, The axial vector current in beta decay, Nuovo Cimento 16, 705 (1960).
  2. Daniel Harry Friedan, Nonlinear models in Two + Epsilon dimensions, Ann. Phys. (N.Y.) 163, 318 (1985).
  3. V. E. Zakharov and A. V. Mikhailov, Relativistically invariant two-dimensional models in field theory integrable by the inverse problem technique, Sov. Phys. JETP 47, 1017 (1978).
  4. H. Eichenherr and M. Forger, On the dual symmetry of the nonlinear sigma models, Nucl. Phys. B155, 381 (1979).
  5. Ben Hoare, Integrable deformations of sigma models, J. Phys. A 55, 093001 (2022).
  6. Alexander B. Zamolodchikov and Alexei B. Zamolodchikov, Factorized S matrices in two dimensions as the exact solutions of certain relativistic quantum field models, Ann. Phys. (N.Y.) 120, 253 (1979).
  7. A. A. Belavin and V. G. Drinfel’d, Solutions of the classical Yang-Baxter equation for simple Lie algebras, Funct. Anal. Appl. 16, 159 (1982).
  8. V. V. Bazhanov, Trigonometric solution of triangle equations and classical lie algebras, Phys. Lett. B 159, 321 (1985).
  9. Michio Jimbo, Quantum R Matrix for the generalized toda system, Commun. Math. Phys. 102, 537 (1986).
  10. V. A. Fateev, E. Onofri, and Alexei B. Zamolodchikov, Integrable deformations of the O(3) sigma model. The sausage model, Nucl. Phys. B406, 521 (1993).
  11. V. A. Fateev, The duality between two-dimensional integrable field theories and sigma models, Phys. Lett. B 357, 397 (1995).
  12. Ctirad Klimcik, On integrability of the Yang-Baxter sigma-model, J. Math. Phys. (N.Y.) 50, 043508 (2009).
  13. Francois Delduc, Marc Magro, and Benoit Vicedo, On classical q-deformations of integrable sigma-models, J. High Energy Phys. 11 (2013) 192.
  14. V. A. Fateev and A. V. Litvinov, Integrability, duality and sigma models, J. High Energy Phys. 11 (2018) 204.
  15. A. V. Litvinov and L. A. Spodyneiko, On dual description of the deformed O(N) sigma model, J. High Energy Phys. 11 (2018) 139.
  16. Mikhail Alfimov et al., Dual description of η-deformed OSP sigma models, J. High Energy Phys. 12 (2020) 040.
  17. Alexey Bychkov and Alexey Litvinov, On dual regime in Yang-Baxter deformed O(2N) sigma models, J. High Energy Phys. 10 (2025) 080.
  18. Vladimir Fateev, Classical and quantum integrable sigma models. Ricci Flow, “Nice Duality” and perturbed rational conformal field theories, J. Exp. Theor. Phys. 129, 566 (2019).
  19. Sidney Coleman, Quantum sine-Gordon equation as the massive Thirring model, Phys. Rev. D 11, 2088 (1975).
  20. S. Mandelstam, Soliton operators for the quantized sine-Gordon equation, Phys. Rev. D 11, 3026 (1975).
  21. Diego Bombardelli, Lectures on S-matrices and integrability, arXiv:1606.02949.
  22. Alexei B. Zamolodchikov, Mass scale in the sine-Gordon model and its reductions, Int. J. Mod. Phys. A 10, 1125 (1995).

Outline

Information

Phys. Rev. D 113, 066007– Published 11 March, 2026
  • Received 25 October 2025
  • Accepted 18 February 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