Integrability of the bi-Yang-Baxter \(\sigma\)-model. (English) Zbl 1359.70102
Summary: We construct a Lax pair with spectral parameter for a two-parameter doubly Poisson-Lie deformation of the principal chiral model.
MSC:
| 70S10 | Symmetries and conservation laws in mechanics of particles and systems |
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
| 70H06 | Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
References:
| [1] | Arutyunov, G., Borsato, R., Frolov, S.: S-matrix for strings on η-deformed AdS5 × S5. arXiv:1312.3542 [hep-th] · Zbl 1388.83726 |
| [2] | Balog, J., Forgács, P., Horváth, Z., Palla, L.: A new family of SU(2) symmetric integrable σ-models. Phys. Lett. B 324, 403 (1994). hep-th/9307030 · Zbl 0957.81660 |
| [3] | Cherednik I.V.: Relativistically invariant quasiclassical limits of integrable two-dimensional quantum models. Theor. Math. Phys. 47, 422 (1981) · doi:10.1007/BF01086395 |
| [4] | Delduc, F., Magro, M., Vicedo, B.: On classical q-deformations of integrable sigma-models. JHEP 11, 192 (2013). arXiv:1308.3581 [hep-th] · Zbl 1342.81182 |
| [5] | Delduc, F., Magro, M., Vicedo, B.: An integrable deformation of the AdS5 × S5 superstring action. arXiv:1309.5850 [hep-th] · Zbl 1333.81322 |
| [6] | Delduc, F.: Some integrable deformations of non-linear sigma-models. http://www.itp.uni-hannover.de/ lechtenf/sis13/sistalks/delduc |
| [7] | Devchand, C., Schiff, J.: Hidden symmetries of the principal chiral model unveiled. Commun. Math. Phys. 190, 675 (1998). hep-th/9611081 · Zbl 0908.35107 |
| [8] | Evans, J.M., Hollowood, T.J.: Integrable theories that are asymptotically CFT. Nucl. Phys. B 438, 469 (1995). hep-th/9407113 · Zbl 1052.81605 |
| [9] | Kawaguchi, I., Yoshida, K.: Hybrid classical integrability in squashed sigma models. Phys. Lett. B 705, 251 (2011). arXiv:1107.3662 [hep-th] |
| [10] | Kawaguchi, I., Matsumoto, T., Yoshida, K.: On the classical equivalence of monodromy matrices in squashed sigma model. JHEP 1206, 082 (2012). arXiv:1203.3400 [hep-th] · Zbl 1397.81264 |
| [11] | Kawaguchi, I., Matsumoto, T., Yoshida, K.: Jordanian deformations of the AdS5 × S5 superstring. arXiv:1401.4855 [hep-th] |
| [12] | Klimčí k, C., Ševera, P.: Dual non-Abelian duality and the Drinfeld double. Phys. Lett. B 351, 455 (1995). hep-th/9502122 |
| [13] | Klimčí k, C.: Poisson-Lie T-duality. Nucl. Phys. B (Proc. Suppl.) 46, 116 (1996). hep-th/9509095 · Zbl 0957.81598 |
| [14] | Ševera, P.: Minimálne plochy a dualita, Diploma thesis (in Slovak) (1995) |
| [15] | Klimčí k, C., Ševera, P.: T-duality and the moment map. In: Cargese 1996, Quantum Fields and Quantum Space Time, p. 323. hep-th/9610198 · Zbl 0924.58132 |
| [16] | Klimčí k, C.: Yang-Baxter σ-models and dS/AdS T-duality. JHEP 0212, 051 (2002). hep-th/0210095 · Zbl 0677.58020 |
| [17] | Klimčí k, C.: On integrability of the Yang-Baxter σ-model. J. Math. Phys. 50, 043508 (2009). arXiv:0802.3518 [hep-th] · Zbl 1215.81099 |
| [18] | Mañas M.: The principal chiral model as an integrable system. Aspects Math. E 23,147 (1994) · Zbl 0801.58022 · doi:10.1007/978-3-663-14092-4_7 |
| [19] | Mohammedi, N.: On the geometry of classical integrable two-dimensional nonlinear σ-models, Nucl. Phys. B 839, 420 (2010). arXiv:0806.0550 [hep-th] · Zbl 1206.37038 |
| [20] | Reiman, A.G., Semenov Tian-Shansky, M.A.: Integrable systems, Sovremennaja matematika, Moskva-Izhevsk (in russian) (2003) · Zbl 0801.58022 |
| [21] | Spradlin, M., Volovich, A.: Dressing the Giant Magnon. JHEP 0610, 012 (2006). hep-th/0607009 · Zbl 1246.81265 |
| [22] | Semenov-Tian-Shansky, M.: Dressing transformations and Poisson groups actions. Publ. RIMS, vol. 21. Kyoto Univ, p. 1237 (1985) · Zbl 0673.58019 |
| [23] | Sfetsos, K.: Integrable interpolations: from exact CFTs to non-Abelian T-duals. arXiv:1312.4560 [hep-th] · Zbl 1284.81257 |
| [24] | Uhlenbeck K.: Harmonic maps into Lie groups (classical solutions of the chiral model). J. Differ. Geom. 30, 1 (1989) · Zbl 0677.58020 |
| [25] | Zakharov V.E., Mikhailov A.V.: Relativistically invariant two-dimensional model of field theory which is integrable by means of the inverse scattering method. Sov. Phys. JETP 47, 1017 (1978) |
| [26] | Zhelobenko, D.P.: Compact Lie groups and their representations, Translations of Mathematical Monographs, vol. 40. AMS, Providence (1973) · Zbl 0228.22013 |
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