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Asymptotics in the bi-Yang-Baxter sigma model

Meer Ashwinkumar1, Domenico Orlando2,1,3, Susanne Reffert1,3, and Giacomo Sberveglieri1

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Phys. Rev. D 112, 125023 – Published 19 December, 2025

DOI: https://doi.org/10.1103/rxks-rk37

Abstract

Working in a sector of large charge is a powerful tool to analytically access models that are either strongly coupled or otherwise difficult to solve explicitly. In the context of integrable systems, Volin’s method is exactly such a large-charge approach. In this note, we apply this method to the bi-Yang-Baxter deformed SU(2) principal chiral model. Our main result is an explicit expression for the free energy density as an asymptotic expansion. We moreover determine the leading nonperturbative effects both via analytic methods and a resurgence analysis.

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References (62)

  1. S. Hellerman, D. Orlando, S. Reffert, and M. Watanabe, On the CFT operator spectrum at large global charge, J. High Energy Phys. 12 (2015) 071.
  2. A. Monin, D. Pirtskhalava, R. Rattazzi, and F. K. Seibold, Semiclassics, Goldstone bosons and CFT data, J. High Energy Phys. 06 (2017) 011.
  3. L. A. Gaumé, D. Orlando, and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rep. 933, 1 (2021).
  4. L. Alvarez-Gaume, D. Orlando, and S. Reffert, Large charge at large N, J. High Energy Phys. 12 (2019) 142.
  5. N. Dondi, I. Kalogerakis, D. Orlando, and S. Reffert, Resurgence of the large-charge expansion, J. High Energy Phys. 05 (2021) 035.
  6. N. Dondi, S. Hellerman, I. Kalogerakis, R. Moser, D. Orlando, and S. Reffert, Fermionic CFTs at large charge and large N, J. High Energy Phys. 08 (2023) 180.
  7. G. Badel, G. Cuomo, A. Monin, and R. Rattazzi, The epsilon expansion meets semiclassics, J. High Energy Phys. 11 (2019) 110.
  8. M. Watanabe, Accessing large global charge via the ε-expansion, J. High Energy Phys. 04 (2021) 264.
  9. G. Arias-Tamargo, D. Rodriguez-Gomez, and J. G. Russo, The large charge limit of scalar field theories and the Wilson-Fisher fixed point at ε=0, J. High Energy Phys. 10 (2019) 201.
  10. S. Hellerman and S. Maeda, On the large R-charge expansion in N=2 superconformal field theories, J. High Energy Phys. 12 (2017) 135.
  11. S. Hellerman, S. Maeda, D. Orlando, S. Reffert, and M. Watanabe, Universal correlation functions in rank 1 SCFTs, J. High Energy Phys. 12 (2019) 047.
  12. S. Hellerman, S. Maeda, D. Orlando, S. Reffert, and M. Watanabe, S-duality and correlation functions at large R-charge, J. High Energy Phys. 04 (2021) 287.
  13. Z. Komargodski, M. Mezei, S. Pal, and A. Raviv-Moshe, Spontaneously broken boosts in CFTs, J. High Energy Phys. 09 (2021) 064.
  14. T. Araujo, O. Celikbas, D. Orlando, and S. Reffert, 2D CFTs: Large charge is not enough, Phys. Rev. D 105, 086029 (2022).
  15. M. Dodelson, S. Hellerman, M. Watanabe, and M. Yamazaki, Integrability of large-charge sectors in generic 2D EFTs, J. High Energy Phys. 08 (2024) 166.
  16. C. Klimcik, Yang-Baxter sigma models and dS/AdS T duality, J. High Energy Phys. 12 (2002) 051.
  17. C. Klimcik, On integrability of the Yang-Baxter sigma-model, J. Math. Phys. (N.Y.) 50, 043508 (2009).
  18. C. Klimcik, Integrability of the bi-Yang-Baxter sigma-model, Lett. Math. Phys. 104, 1095 (2014).
  19. D. Volin, Quantum integrability and functional equations: Applications to the spectral problem of AdS/CFT and two-dimensional sigma models, J. Phys. A 44, 124003 (2011).
  20. D. Volin, From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigmamodels, Phys. Rev. D 81, 105008 (2010).
  21. V. A. Fateev, The sigma model (dual) representation for a two-parameter family of integrable quantum field theories, Nucl. Phys. B473, 509 (1996).
  22. B. Hoare, R. Roiban, and A. A. Tseytlin, On deformations of AdSn x Sn supercosets, J. High Energy Phys. 06 (2014) 002.
  23. L. Schepers and D. C. Thompson, Resurgence in the bi-Yang-Baxter model, Nucl. Phys. B964, 115308 (2021).
  24. B. Hoare, Integrable deformations of sigma models, J. Phys. A 55, 093001 (2022).
  25. R. Squellari, Yang-Baxter σ model: Quantum aspects, Nucl. Phys. B881, 502 (2014).
  26. K. Sfetsos, K. Siampos, and D. C. Thompson, Generalised integrable λ—and η-deformations and their relation, Nucl. Phys. B899, 489 (2015).
  27. A. M. Polyakov and P. B. Wiegmann, Theory of non-Abelian Goldstone Bosons, Phys. Lett. 131B, 121 (1983).
  28. P. B. Wiegmann, Exact solution of the O(3) nonlinear sigma model, Phys. Lett. B 152B, 209 (1985).
  29. P. Hasenfratz, M. Maggiore, and F. Niedermayer, The exact mass gap of the O(3) and O(4) nonlinear sigma models in d=2, Phys. Lett. B 245, 522 (1990).
  30. P. Hasenfratz and F. Niedermayer, The exact mass gap of the O(N) sigma model for arbitrary N is >=3 in d =2, Phys. Lett. B 245, 529 (1990).
  31. P. Forgacs, F. Niedermayer, and P. Weisz, The exact mass gap of the Gross-Neveu model. 1. The thermodynamic Bethe Ansatz, Nucl. Phys. B367, 123 (1991).
  32. P. Forgacs, F. Niedermayer, and P. Weisz, The exact mass gap of the Gross-Neveu model. 2. The 1/N expansion, Nucl. Phys. B367, 144 (1991).
  33. J. Balog, S. Naik, F. Niedermayer, and P. Weisz, Exact mass gap of the chiral SU(n) x SU(n) model, Phys. Rev. Lett. 69, 873 (1992).
  34. T. J. Hollowood, The exact mass gaps of the principal chiral models, Phys. Lett. B 329, 450 (1994).
  35. J. M. Evans and T. J. Hollowood, The exact mass gap of the supersymmetric o(N) sigma model, Phys. Lett. B 343, 189 (1995).
  36. J. M. Evans and T. J. Hollowood, The exact mass gap of the supersymmetric CPN–1 sigma model, Phys. Lett. B 343, 198 (1995).
  37. J. M. Evans and T. J. Hollowood, Exact results for integrable asymptotically—free field theories, Nucl. Phys. B, Proc. Suppl. 45, 130 (1996).
  38. V. A. Fateev, V. A. Kazakov, and P. B. Wiegmann, Large N chiral field in two-dimensions, Phys. Rev. Lett. 73, 1750 (1994).
  39. V. A. Fateev, V. A. Kazakov, and P. B. Wiegmann, Principal chiral field at large N, Nucl. Phys. B424, 505 (1994).
  40. K. Zarembo, Quantum giant magnons, J. High Energy Phys. 05 (2008) 047.
  41. M. Mariño and T. Reis, Resurgence for superconductors, J. Stat. Mech. (2019) 123102.
  42. M. Mariño and T. Reis, Renormalons in integrable field theories, J. High Energy Phys. 04 (2020) 160.
  43. M. C. Abbott, Z. Bajnok, J. Balog, and A. Hegedús, From perturbative to non-perturbative in the O (4) sigma model, Phys. Lett. B 818, 136369 (2021).
  44. M. C. Abbott, Z. Bajnok, J. Balog, A. Hegedús, and S. Sadeghian, Resurgence in the O(4) sigma model, J. High Energy Phys. 05 (2021) 253.
  45. M. Marino, R. Miravitllas, and T. Reis, Testing the Bethe Ansatz with large N renormalons, Eur. Phys. J. Special Topics 230, 2641 (2021).
  46. L. Di Pietro, M. Mariño, G. Sberveglieri, and M. Serone, Resurgence and 1/N expansion in integrable field theories, J. High Energy Phys. 10 (2021) 166.
  47. M. Marino, R. Miravitllas, and T. Reis, New renormalons from analytic trans-series, J. High Energy Phys. 08 (2022) 279.
  48. Z. Bajnok, J. Balog, and I. Vona, Analytic resurgence in the O(4) model, J. High Energy Phys. 04 (2022) 043.
  49. Z. Bajnok, J. Balog, A. Hegedus, and I. Vona, Instanton effects vs resurgence in the O(3) sigma model, Phys. Lett. B 829, 137073 (2022).
  50. M. Marino, R. Miravitllas, and T. Reis, Instantons, renormalons and the theta angle in integrable sigma models, SciPost Phys. 15, 184 (2023).
  51. Z. Bajnok, J. Balog, A. Hegedus, and I. Vona, Running coupling and non-perturbative corrections for O(N) free energy and for disk capacitor, J. High Energy Phys. 09 (2022) 001.
  52. Z. Bajnok, J. Balog, and I. Vona, The full analytic trans-series in integrable field theories, Phys. Lett. B 844, 138075 (2023).
  53. L. Schepers and D. C. Thompson, Asymptotics in an asymptotic CFT, J. High Energy Phys. 04 (2023) 112.
  54. Z. Bajnok, J. Balog, and I. Vona, The complete trans-series for conserved charges in integrable field theories, Ann. Phys. (Amsterdam) 481, 170152 (2025).
  55. E Hopf and N Wiener, Über eine klasse singulärer integralgleichungen, Sitzungsber. Preuß. Akad. Wiss. Berlin XXXI, 696 (1931).
  56. T. Reis, On the resurgence of renormalons in integrable theories, Ph.D. thesis, U. Geneva (main), 2022, arXiv:2209.15386.
  57. D. Sauzin, Variations on the resurgence of the Gamma function, arXiv:2112.15226.
  58. B. Hoare and A. A. Tseytlin, On integrable deformations of superstring sigma models related to AdSn×Sn supercosets, Nucl. Phys. B897, 448 (2015).
  59. C. Klimcik, η and λ deformations as E-models, Nucl. Phys. B900, 259 (2015).
  60. B. Hoare, Towards a two-parameter q-deformation of AdS3×S3×M4 superstrings, Nucl. Phys. B891, 259 (2015).
  61. F. Delduc, M. Magro, and B. Vicedo, An integrable deformation of the AdS5×S5 superstring action, Phys. Rev. Lett. 112, 051601 (2014).
  62. A. B. Zamolodchikov, Mass scale in the Sine-Gordon model and its reductions, Int. J. Mod. Phys. A 10, 1125 (1995).

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Phys. Rev. D 112, 125023– Published 19 December, 2025
  • Received 24 May 2025
  • Accepted 24 November 2025
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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.

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