Abstract
A multi-parameter integrable deformation of the principal chiral model is presented. The Yang-Baxter and bi-Yang-Baxter σ-models, the principal chiral model plus a Wess-Zumino term and the TsT transformation of the principal chiral model are all recovered when the appropriate deformation parameters vanish. When the Lie group is SU(2), we show that this four-parameter integrable deformation of the SU(2) principal chiral model corresponds to the Lukyanov model.
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References
S.L. Lukyanov, The integrable harmonic map problem versus Ricci flow, Nucl. Phys. B 865 (2012) 308 [arXiv:1205.3201] [INSPIRE].
B. Hoare, R. Roiban and A.A. Tseytlin, On deformations of AdS n × S n supercosets, JHEP 06 (2014) 002 [arXiv:1403.5517] [INSPIRE].
V.A. Fateev, The σ-model (dual) representation for a two-parameter family of integrable quantum field theories, Nucl. Phys. B 473 (1996) 509 [INSPIRE].
E. Witten, Nonabelian Bosonization in Two-Dimensions, Commun. Math. Phys. 92 (1984) 455 [INSPIRE].
J.H. Horne and G.T. Horowitz, Exact black string solutions in three-dimensions, Nucl. Phys. B 368 (1992) 444 [hep-th/9108001] [INSPIRE].
A. Giveon and M. Roček, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [hep-th/9112070] [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].
C. Klimčík, Integrability of the bi-Yang-Baxter σ-model, Lett. Math. Phys. 104 (2014) 1095 [arXiv:1402.2105] [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, 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].
I. Kawaguchi and K. Yoshida, Hybrid classical integrability in squashed σ-models, Phys. Lett. B 705 (2011) 251 [arXiv:1107.3662] [INSPIRE].
F. Delduc, S. Lacroix, M. Magro and B. Vicedo, On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models, J. Phys. A 49 (2016) 415402 [arXiv:1606.01712] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, Integrable double deformation of the principal chiral model, Nucl. Phys. B 891 (2015) 312 [arXiv:1410.8066] [INSPIRE].
I. Kawaguchi, D. Orlando and K. Yoshida, Yangian symmetry in deformed WZNW models on squashed spheres, Phys. Lett. B 701 (2011) 475 [arXiv:1104.0738] [INSPIRE].
I. Kawaguchi and K. Yoshida, A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models, J. Math. Phys. 55 (2014) 062302 [arXiv:1311.4696] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5 × S 5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [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, Schrödinger geometries arising from Yang-Baxter deformations, JHEP 04 (2015) 180 [arXiv:1502.00740] [INSPIRE].
T. Matsumoto and K. Yoshida, Integrability of classical strings dual for noncommutative gauge theories, JHEP 06 (2014) 163 [arXiv:1404.3657] [INSPIRE].
T. Matsumoto and K. Yoshida, Yang-Baxter σ-models based on the CYBE, Nucl. Phys. B 893 (2015) 287 [arXiv:1501.03665] [INSPIRE].
S.J. van Tongeren, On classical Yang-Baxter based deformations of the AdS 5 × S 5 superstring, JHEP 06 (2015) 048 [arXiv:1504.05516] [INSPIRE].
S.J. van Tongeren, Yang-Baxter deformations, AdS/CFT and twist-noncommutative gauge theory, Nucl. Phys. B 904 (2016) 148 [arXiv:1506.01023] [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].
B. Hoare, Towards a two-parameter q-deformation of AdS 3 × S 3 × M 4 superstrings, Nucl. Phys. B 891 (2015) 259 [arXiv:1411.1266] [INSPIRE].
C. Klimčík and A.A. Tseytlin, Duality invariant class of exact string backgrounds, Phys. Lett. B 323 (1994) 305 [hep-th/9311012] [INSPIRE].
S.A. Frolov, R. Roiban and A.A. Tseytlin, Gauge-string duality for superconformal deformations of N = 4 super Yang-Mills theory, JHEP 07 (2005) 045 [hep-th/0503192] [INSPIRE].
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].
D. Bykov, Complex structure-induced deformations of σ-models, JHEP 03 (2017) 130 [arXiv:1611.07116] [INSPIRE].
A.M. Polyakov and P.B. Wiegmann, Theory of Nonabelian Goldstone Bosons, Phys. Lett. B 131 (1983) 121 [INSPIRE].
B. Vicedo, Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles, J. Phys. A 48 (2015) 355203 [arXiv:1504.06303] [INSPIRE].
F. Delduc, T. Kameyama, M. Magro and B. Vicedo, Affine q-deformed symmetry and the classical Yang-Baxter σ-model, JHEP 03 (2017) 126 [arXiv:1701.03691] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, The classical origin of quantum affine algebra in squashed σ-models, JHEP 04 (2012) 115 [arXiv:1201.3058] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, On the classical equivalence of monodromy matrices in squashed σ-model, JHEP 06 (2012) 082 [arXiv:1203.3400] [INSPIRE].
B. Vicedo, On integrable field theories as dihedral affine Gaudin models, arXiv:1701.04856 [INSPIRE].
C. Klimčík, Yang-Baxter σ-model with WZNW term as ℰ -model, Phys. Lett. B 772 (2017) 725 [arXiv:1706.08912] [INSPIRE].
C. Klimčík, η and λ deformations as ℰ -models, Nucl. Phys. B 900 (2015) 259 [arXiv:1508.05832] [INSPIRE].
C. Klimčík, Poisson-Lie T-duals of the bi-Yang-Baxter models, Phys. Lett. B 760 (2016) 345 [arXiv:1606.03016] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach, Superstring theory on AdS 2 × S 2 as a coset supermanifold, Nucl. Phys. B 567 (2000) 61 [hep-th/9907200] [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
K. Zarembo, Strings on Semisymmetric Superspaces, JHEP 05 (2010) 002 [arXiv:1003.0465] [INSPIRE].
L. Wulff, On integrability of strings on symmetric spaces, JHEP 09 (2015) 115 [arXiv:1505.03525] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS 5 × S 5 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 AdS 5 × S 5 superstring, JHEP 10 (2014) 132 [arXiv:1406.6286] [INSPIRE].
A. Babichenko, B. Stefanski Jr. and K. Zarembo, Integrability and the AdS 3 /CF T 2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [INSPIRE].
A. Cagnazzo and K. Zarembo, B-field in AdS 3 /CF T 2 Correspondence and Integrability, JHEP 11 (2012) 133 [Erratum ibid. 04 (2013) 003] [arXiv:1209.4049] [INSPIRE].
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Delduc, F., Hoare, B., Kameyama, T. et al. Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable σ-model. J. High Energ. Phys. 2017, 212 (2017). https://doi.org/10.1007/JHEP10(2017)212
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DOI: https://doi.org/10.1007/JHEP10(2017)212