Abstract
We derive the Faddeev-Reshetikhin (FR) model from a four-dimensional Chern-Simons theory with two order surface defects by following the work by Costello and Yamazaki [arXiv:1908.02289]. Then we present a trigonometric deformation of the FR model by employing a boundary condition with an R-operator of Drinfeld-Jimbo type. This is a generalization of the work by Delduc, Lacroix, Magro and Vicedo [arXiv:1909.13824] from the disorder surface defect case to the order one.
Article PDF
Similar content being viewed by others
References
K. Costello, Supersymmetric gauge theory and the Yangian, arXiv:1303.2632 [INSPIRE].
K. Costello, E. Witten and M. Yamazaki, Gauge theory and integrability, I, ICCM Not. 06 (2018) 46 [arXiv:1709.09993] [INSPIRE].
K. Costello, E. Witten and M. Yamazaki, Gauge theory and integrability, II, ICCM Not. 06 (2018) 120 [arXiv:1802.01579] [INSPIRE].
K. Costello and M. Yamazaki, Gauge theory and integrability, III, arXiv:1908.02289 [INSPIRE].
B. Vicedo, Holomorphic Chern-Simons theory and affine Gaudin models, arXiv:1908.07511 [INSPIRE].
F. Delduc, S. Lacroix, M. Magro and B. Vicedo, A unifying 2d action for integrable σ-models from 4d Chern-Simons theory, arXiv:1909.13824 [INSPIRE].
O. Fukushima, J.-i. Sakamoto and K. Yoshida, Comments on η-deformed principal chiral model from 4D Chern-Simons theory, Nucl. Phys. B 957 (2020) 115080 [arXiv:2003.07309] [INSPIRE].
O. Fukushima, J.-i. Sakamoto and K. Yoshida, Yang-Baxter deformations of the AdS5 × S5 supercoset σ-model from 4D Chern-Simons theory, JHEP 09 (2020) 100 [arXiv:2005.04950] [INSPIRE].
D. M. Schmidtt, Holomorphic Chern-Simons theory and lambda models: PCM case, JHEP 04 (2020) 060 [arXiv:1912.07569] [INSPIRE].
J. Tian, Comments on λ-deformed models from 4D Chern-Simons theory, arXiv:2005.14554 [INSPIRE].
J. Tian, Y.-J. He and B. Chen, λ-deformed AdS5 × S5 superstring from 4D Chern-Simons theory, arXiv:2007.00422 [INSPIRE].
B. Hoare and S. Lacroix, Yang-Baxter deformations of the principal chiral model plus Wess-Zumino term, J. Phys. A 53 (2020) 505401 [arXiv:2009.00341] [INSPIRE].
S. Lacroix and B. Vicedo, Integrable ℰ-models, 4d Chern-Simons theory and affine Gaudin models, I — Lagrangian aspects, arXiv:2011.13809 [INSPIRE].
K. Costello and B. Stefański, Chern-Simons origin of superstring integrability, Phys. Rev. Lett. 125 (2020) 121602 [arXiv:2005.03064] [INSPIRE].
D. Gaiotto, J. H. Lee and J. Wu, Integrable Kondo problems, arXiv:2003.06694 [INSPIRE].
D. Gaiotto, J. H. Lee, B. Vicedo and J. Wu, Kondo line defects and affine Gaudin models, arXiv:2010.07325 [INSPIRE].
R. Bittleston and D. Skinner, Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory, arXiv:2011.04638 [INSPIRE].
L. D. Faddeev and N. Y. Reshetikhin, Integrability of the principal chiral field model in (1 + 1)-dimension, Annals Phys. 167 (1986) 227.
V. G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl. 32 (1985) 254 [Dokl. Akad. Nauk Ser.Fiz. 283 (1985) 1060] [INSPIRE].
M. Jimbo, A q difference analog of U (g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985) 63 [INSPIRE].
V. Caudrelier, M. Stoppato and B. Vicedo, On the Zakharov-Mikhailov action: 4d Chern-Simons origin and covariant Poisson algebra of the Lax connection, arXiv:2012.04431 [INSPIRE].
M. Benini, A. Schenkel and B. Vicedo, Homotopical analysis of 4d Chern-Simons theory and integrable field theories, arXiv:2008.01829 [INSPIRE].
C. Appadu, T. J. Hollowood and D. Price, Quantum inverse scattering and the Lambda deformed principal chiral model, J. Phys. A 50 (2017) 305401 [arXiv:1703.06699] [INSPIRE].
T. Klose and K. Zarembo, Bethe ansatz in stringy σ-models, J. Stat. Mech. 0605 (2006) P05006 [hep-th/0603039] [INSPIRE].
K. Costello and J. Yagi, Unification of integrability in supersymmetric gauge theories, arXiv:1810.01970 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2012.07370
Rights and permissions
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.
About this article
Cite this article
Fukushima, O., Sakamoto, Ji. & Yoshida, K. Faddeev-Reshetikhin model from a 4D Chern-Simons theory. J. High Energ. Phys. 2021, 115 (2021). https://doi.org/10.1007/JHEP02(2021)115
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2021)115