Abstract
We present homogeneous Yang-Baxter deformations of the AdS5×S5 supercoset sigma model as boundary conditions of a 4D Chern-Simons theory. We first generalize the procedure for the 2D principal chiral model developed by Delduc et al. [5] so as to reproduce the 2D symmetric coset sigma model, and specify boundary conditions governing homogeneous Yang-Baxter deformations. Then the conditions are applicable for the AdS5×S5 supercoset sigma model case as well. In addition, homogeneous bi-Yang-Baxter deformation is also discussed.
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K. Costello, E. Witten and M. Yamazaki, Gauge theory and integrability, I, arXiv:1709.09993 [INSPIRE].
K. Costello, E. Witten and M. Yamazaki, Gauge theory and integrability, II, 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].
C. Klimčík, Yang-Baxter σ-models and dS/AdS T duality, JHEP 12 (2002) 051 [hep-th/0210095] [INSPIRE].
C. Klimčík, On integrability of the Yang-Baxter σ-model, J. Math. Phys. 50 (2009) 043508 [arXiv:0802.3518] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable σ-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS5 ×S5 superstring action, Phys. Rev. Lett. 112 (2014) 051601 [arXiv:1309.5850] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, Derivation of the action and symmetries of the q-deformed AdS5 ×S5 superstring, JHEP 10 (2014) 132 [arXiv:1406.6286] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS5 ×S5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [INSPIRE].
T. Matsumoto and K. Yoshida, Yang-Baxter σ-models based on the CYBE, Nucl. Phys. B 893 (2015) 287 [arXiv:1501.03665] [INSPIRE].
K. Sfetsos, Integrable interpolations: from exact CFTs to non-Abelian T-duals, Nucl. Phys. B 880 (2014) 225 [arXiv:1312.4560] [INSPIRE].
T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, Integrable deformations of strings on symmetric spaces, JHEP 11 (2014) 009 [arXiv:1407.2840] [INSPIRE].
D.M. Schmidtt, Holomorphic Chern-Simons theory and lambda models: PCM case, JHEP 04 (2020) 060 [arXiv:1912.07569] [INSPIRE].
C. Bassi and S. Lacroix, Integrable deformations of coupled σ-models, JHEP 05 (2020) 059 [arXiv:1912.06157] [INSPIRE].
K. Costello and B. Stefański, The Chern-Simons origin of superstring integrability, arXiv:2005.03064 [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].
F. Delduc, S. Lacroix, M. Magro and B. Vicedo, On the Hamiltonian integrability of the bi-Yang-Baxter σ-model, JHEP 03 (2016) 104 [arXiv:1512.02462] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS5 ×S5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
H. Itoyama and T. Oota, The AdS5 ×S5 superstrings in the generalized light-cone gauge, Prog. Theor. Phys. 117 (2007) 957 [hep-th/0610325] [INSPIRE].
B. Vicedo, Hamiltonian dynamics and the hidden symmetries of the AdS5 ×S5 superstring, JHEP 01 (2010) 102 [arXiv:0910.0221] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS5 ×S5 superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS5 ×S5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
O. Fukushima, J. Sakamoto and K. Yoshida, in preparation.
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].
L.F. Alday, G. Arutyunov and S. Frolov, Green-Schwarz strings in TsT-transformed backgrounds, JHEP 06 (2006) 018 [hep-th/0512253] [INSPIRE].
T. Matsumoto and K. Yoshida, Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence, JHEP 06 (2014) 135 [arXiv:1404.1838] [INSPIRE].
T. Matsumoto and K. Yoshida, Integrability of classical strings dual for noncommutative gauge theories, JHEP 06 (2014) 163 [arXiv:1404.3657] [INSPIRE].
D. Osten and S.J. van Tongeren, Abelian Yang-Baxter deformations and TsT transformations, Nucl. Phys. B 915 (2017) 184 [arXiv:1608.08504] [INSPIRE].
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ArXiv ePrint: 2005.04950
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Fukushima, O., Sakamoto, Ji. & Yoshida, K. Yang-Baxter deformations of the AdS5×S5 supercoset sigma model from 4D Chern-Simons theory. J. High Energ. Phys. 2020, 100 (2020). https://doi.org/10.1007/JHEP09(2020)100
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DOI: https://doi.org/10.1007/JHEP09(2020)100