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Yang-Baxter sigma models based on the CYBE. (English) Zbl 1348.81379
Summary: It is known that Yang-Baxter sigma models provide a systematic way to study integrable deformations of both principal chiral models and symmetric coset sigma models. In the original proposal and its subsequent development, the deformations have been characterized by classical \(r\)-matrices satisfying the modified classical Yang-Baxter equation (mCYBE). In this article, we propose the Yang-Baxter sigma models based on the classical Yang-Baxter equations (CYBE) rather than the mCYBE. This generalization enables us to utilize various kinds of solutions of the CYBE to classify integrable deformations. In particular, it is straightforward to realize partial deformations of the target space without loss of the integrability of the parent theory.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
16T25 Yang-Baxter equations
81R12 Groups and algebras in quantum theory and relations with integrable systems
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References:
[1] Maldacena, J. M., The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., Int. J. Theor. Phys., 38, 1113, (1999) · Zbl 0969.81047
[2] Beisert, N., Review of AdS/CFT integrability: an overview, Lett. Math. Phys., 99, 3, (2012)
[3] Bena, I.; Polchinski, J.; Roiban, R., Hidden symmetries of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring, Phys. Rev. D, 69, 046002, (2004)
[4] Metsaev, R. R.; Tseytlin, A. A., Type IIB superstring action in \(\operatorname{AdS}_5 \times \operatorname{S}^5\) background, Nucl. Phys. B, 533, 109, (1998) · Zbl 0956.81063
[5] Minahan, J. A.; Zarembo, K., The Bethe ansatz for \(N = 4\) superyang-Mills, J. High Energy Phys., 0303, 013, (2003)
[6] Beisert, N.; Koroteev, P., Quantum deformations of the one-dimensional Hubbard model, J. Phys. A, 41, 255204, (2008) · Zbl 1163.81009
[7] Beisert, N.; Galleas, W.; Matsumoto, T., A quantum affine algebra for the deformed Hubbard chain, J. Phys. A, 45, 365206, (2012) · Zbl 1280.17015
[8] Klimcik, C., Yang-Baxter sigma models and ds/AdS T duality, J. High Energy Phys., 0212, 051, (2002)
[9] Klimcik, C., On integrability of the Yang-Baxter sigma-model, J. Math. Phys., 50, 043508, (2009) · Zbl 1215.81099
[10] Klimcik, C., Integrability of the bi-Yang-Baxter sigma-model, Lett. Math. Phys., 104, 1095, (2014) · Zbl 1359.70102
[11] Delduc, F.; Magro, M.; Vicedo, B., On classical q-deformations of integrable sigma-models, J. High Energy Phys., 1311, 192, (2013) · Zbl 1342.81182
[12] Delduc, F.; Magro, M.; Vicedo, B., An integrable deformation of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring action, Phys. Rev. Lett., 112, 051601, (2014) · Zbl 1333.81322
[13] Delduc, F.; Magro, M.; Vicedo, B., Derivation of the action and symmetries of the q-deformed \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring · Zbl 1333.81322
[14] Drinfel’d, V. G., Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl., 32, 254, (1985) · Zbl 0588.17015
[15] Drinfel’d, V. G., Quantum groups, J. Sov. Math., Zap. Nauč. Semin. POMI, 155, 18, (1986) · Zbl 0617.16004
[16] Jimbo, M., A q difference analog of \(U(g)\) and the Yang-Baxter equation, Lett. Math. Phys., 10, 63, (1985) · Zbl 0587.17004
[17] Arutyunov, G.; Borsato, R.; Frolov, S., S-matrix for strings on η-deformed \(\operatorname{AdS}_5 \times \operatorname{S}^5\), J. High Energy Phys., 1404, 002, (2014)
[18] Kawaguchi, I.; Matsumoto, T.; Yoshida, K., Jordanian deformations of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring, J. High Energy Phys., 1404, 153, (2014)
[19] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M.; Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., Integrable deformations of strings on symmetric spaces, J. Phys. A, J. High Energy Phys., 1411, 009, (2014) · Zbl 1333.81341
[20] Sfetsos, K., Integrable interpolations: from exact CFTs to non-abelian T-duals, Nucl. Phys. B, 880, 225, (2014) · Zbl 1284.81257
[21] Lunin, O.; Maldacena, J. M., Deforming field theories with \(U(1) \times U(1)\) global symmetry and their gravity duals, J. High Energy Phys., 0505, 033, (2005)
[22] Frolov, S., Lax pair for strings in lunin-Maldacena background, J. High Energy Phys., 0505, 069, (2005)
[23] Hashimoto, A.; Itzhaki, N., Noncommutative Yang-Mills and the AdS/CFT correspondence, Phys. Lett. B, 465, 142, (1999) · Zbl 0987.81108
[24] Maldacena, J. M.; Russo, J. G., Large N limit of noncommutative gauge theories, J. High Energy Phys., 9909, 025, (1999) · Zbl 0957.81083
[25] Matsumoto, T.; Yoshida, K., Lunin-Maldacena backgrounds from the classical Yang-Baxter equation - towards the gravity/CYBE correspondence, J. High Energy Phys., 1406, 135, (2014) · Zbl 1333.83196
[26] Matsumoto, T.; Yoshida, K., Integrability of classical strings dual for noncommutative gauge theories, J. High Energy Phys., 1406, 163, (2014) · Zbl 1333.81262
[27] Matsumoto, T.; Yoshida, K., Integrable deformations of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring and the classical Yang-Baxter equation - towards the gravity/CYBE correspondence
[28] Kawaguchi, I.; Matsumoto, T.; Yoshida, K., A Jordanian deformation of AdS space in type IIB supergravity, J. High Energy Phys., 1406, 146, (2014) · Zbl 1333.83195
[29] Matsumoto, T.; Yoshida, K., Yang-Baxter deformations and string dualities · Zbl 1388.83865
[30] Crichigno, P. M.; Matsumoto, T.; Yoshida, K., Deformations of \(T^{1, 1}\) as Yang-Baxter sigma models, J. High Energy Phys., 1412, 085, (2014)
[31] Catal-Ozer, A., Lunin-Maldacena deformations with three parameters, J. High Energy Phys., 0602, 026, (2006)
[32] Zakharov, V. E.; Mikhailov, A. V., Relativistically invariant two-dimensional models in field theory integrable by the inverse problem technique, Sov. Phys. JETP, Zh. Eksp. Teor. Fiz., 74, 1953, (1978), (in Russian)
[33] Israel, D.; Kounnas, C.; Orlando, D.; Petropoulos, P. M., Electric/magnetic deformations of S^{3} and AdS(3), and geometric cosets, Fortschr. Phys., 53, 73, (2005) · Zbl 1061.83017
[34] Son, D. T., Toward an AdS/cold atoms correspondence: a geometric realization of the schroedinger symmetry, Phys. Rev. D, 78, 046003, (2008)
[35] Balasubramanian, K.; McGreevy, J., Gravity duals for non-relativistic cfts, Phys. Rev. Lett., 101, 061601, (2008) · Zbl 1228.81247
[36] Kawaguchi, I.; Yoshida, K.; Kawaguchi, I.; Yoshida, K., Exotic symmetry and monodromy equivalence in Schrödinger sigma models, J. High Energy Phys., J. High Energy Phys., 1302, 024, (2013) · Zbl 1342.81240
[37] Kawaguchi, I.; Matsumoto, T.; Yoshida, K., Schroedinger sigma models and Jordanian twists, J. High Energy Phys., 1308, 013, (2013) · Zbl 1342.83108
[38] Schafer-Nameki, S.; Yamazaki, M.; Yoshida, K., Coset construction for duals of non-relativistic cfts, J. High Energy Phys., 0905, 038, (2009)
[39] Hoare, B., Towards a two-parameter q-deformation of \(\operatorname{AdS}_3 \times \operatorname{S}^3 \times \operatorname{M}^4\) superstrings · Zbl 1328.81178
[40] Hoare, B.; Roiban, R.; Tseytlin, A. A., On deformations of \(\operatorname{AdS}_n \times \operatorname{S}^n\) supercosets, J. High Energy Phys., 1406, 002, (2014)
[41] Cherednik, I. V., Relativistically invariant quasiclassical limits of integrable two-dimensional quantum models, Theor. Math. Phys., Teor. Mat. Fiz., 47, 225, (1981)
[42] Faddeev, L. D.; Reshetikhin, N. Y., Integrability of the principal chiral field model in \((1 + 1)\)-dimension, Ann. Phys., 167, 227, (1986)
[43] Balog, J.; Forgacs, P.; Palla, L., A two-dimensional integrable axionic sigma model and T duality, Phys. Lett. B, 484, 367, (2000) · Zbl 1050.81575
[44] Kawaguchi, I.; Yoshida, K.; Kawaguchi, I.; Yoshida, K.; Kawaguchi, I.; Yoshida, K., Hybrid classical integrable structure of squashed sigma models: a short summary, J. High Energy Phys., Phys. Lett. B, J. Phys. Conf. Ser., 343, 012055, (2012)
[45] Kawaguchi, I.; Matsumoto, T.; Yoshida, K.; Kawaguchi, I.; Matsumoto, T.; Yoshida, K., On the classical equivalence of monodromy matrices in squashed sigma model, J. High Energy Phys., J. High Energy Phys., 1206, 082, (2012) · Zbl 1397.81264
[46] Kameyama, T.; Yoshida, K., String theories on warped AdS backgrounds and integrable deformations of spin chains, J. High Energy Phys., 1305, 146, (2013) · Zbl 1342.83385
[47] Orlando, D.; Reffert, S.; Uruchurtu, L. I., Classical integrability of the squashed three-sphere, warped ads_{3} and Schrödinger spacetime via T-duality, J. Phys. A, 44, 115401, (2011) · Zbl 1210.81131
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