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On integrable deformations of superstring sigma models related to \(\mathrm{AdS}_n \times \mathrm{S}^n\) supercosets. (English) Zbl 1329.81317

Summary: We consider two integrable deformations of 2d sigma models on supercosets associated with \(\mathrm{AdS}_n \times \mathrm{S}^n\). The first, the “\(\eta\)-deformation” (based on the Yang-Baxter sigma model), is a one-parameter generalization of the standard superstring action on \(\mathrm{AdS}_n \times \mathrm{S}^n\), while the second, the “\(\lambda\)-deformation” (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the \(\mathrm{AdS}_n \times \mathrm{S}^n\) superstring. We show that the \(\eta\)-deformed model may be obtained from the \(\lambda\)-deformed one by a special scaling limit and analytic continuation in coordinates combined with a particular identification of the parameters of the two models. The relation between the couplings and deformation parameters is consistent with the interpretation of the first model as a real quantum deformation and the second as a root of unity quantum deformation. For the \(\mathrm{AdS}_2 \times \mathrm{S}^2\) case we then explore the effect of this limit on the supergravity background associated with the \(\lambda\)-deformed model. We also suggest that the two models may form a dual Poisson-Lie pair and provide direct evidence for this in the case of the integrable deformations of the coset associated with \(\mathrm{S}^2\).

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T10 Model quantum field theories
81T20 Quantum field theory on curved space or space-time backgrounds
16T25 Yang-Baxter equations
14D15 Formal methods and deformations in algebraic geometry
83E50 Supergravity
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References:

[1] Delduc, F.; Magro, M.; Vicedo, B., Derivation of the action and symmetries of the \(q\)-deformed \(AdS_5 \times S^5\) superstring, J. High Energy Phys., 1410, 132 (2014) · Zbl 1333.81322
[2] Klimcik, C., Yang-Baxter sigma models and dS/AdS T duality, J. High Energy Phys., 0212, 051 (2002)
[3] Klimcik, C., Integrability of the bi-Yang-Baxter sigma-model, Lett. Math. Phys., 104, 1095 (2014) · Zbl 1359.70102
[4] Delduc, F.; Magro, M.; Vicedo, B., On classical \(q\)-deformations of integrable sigma-models, J. High Energy Phys., 1311, 192 (2013) · Zbl 1342.81182
[5] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., Integrable deformations of strings on symmetric spaces, J. High Energy Phys., 1411, 009 (2014) · Zbl 1333.81341
[6] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., An integrable deformation of the \(AdS_5 \times S^5\) superstring, J. Phys. A, 47, 49, 495402 (2014) · Zbl 1305.81120
[7] Sfetsos, K., Integrable interpolations: from exact CFTs to non-Abelian T-duals, Nucl. Phys. B, 880, 225 (2014) · Zbl 1284.81257
[8] Klimcik, C.; Severa, P., Poisson-Lie T duality and loop groups of Drinfeld doubles, Phys. Lett. B, 372, 65 (1996) · Zbl 1037.81576
[9] Klimcik, C.; Severa, P., Dressing cosets, Phys. Lett. B, 381, 56 (1996) · Zbl 0979.81512
[10] Alekseev, A. Y.; Klimcik, C.; Tseytlin, A. A., Quantum Poisson-Lie T duality and WZNW model, Nucl. Phys. B, 458, 430 (1996) · Zbl 1003.81511
[11] Sfetsos, K., Poisson-Lie T duality beyond the classical level and the renormalization group, Phys. Lett. B, 432, 365 (1998)
[12] Squellari, R., Dressing cosets revisited, Nucl. Phys. B, 853, 379 (2011) · Zbl 1229.81258
[13] Hoare, B.; Roiban, R.; Tseytlin, A. A., On deformations of \(AdS_n \times S^n\) supercosets, J. High Energy Phys., 1406, 002 (2014)
[15] Hoare, B.; Hollowood, T. J.; Miramontes, J. L., q-Deformation of the \(AdS_5 \times S^5\) superstring S-matrix and its relativistic limit, J. High Energy Phys., 1203, 015 (2012) · Zbl 1309.81186
[16] Arutyunov, G.; Borsato, R.; Frolov, S., S-matrix for strings on \(η\)-deformed \(AdS_5 \times S^5\), J. High Energy Phys., 1404, 002 (2014)
[17] Engelund, O. T.; Roiban, R., On the asymptotic states and the quantum S matrix of the \(η\)-deformed \(AdS_5 \times S^5\) superstring, J. High Energy Phys., 1503, 168 (2015)
[18] Hoare, B.; Hollowood, T. J.; Miramontes, J. L., Restoring unitarity in the q-deformed world-sheet S-matrix, J. High Energy Phys., 1310, 050 (2013)
[19] Sfetsos, K.; Thompson, D. C., Spacetimes for \(λ\)-deformations, J. High Energy Phys., 1412, 164 (2014)
[20] Demulder, S.; Sfetsos, K.; Thompson, D. C., Integrable \(λ\)-deformations: squashing coset CFTs and \(AdS_5 \times S^5\) · Zbl 1388.83790
[21] Metsaev, R. R.; Tseytlin, A. A., Type IIB superstring action in \(AdS_5 \times S^5\) background, Nucl. Phys. B, 533, 109 (1998) · Zbl 0956.81063
[22] Berkovits, N.; Bershadsky, M.; Hauer, T.; Zhukov, S.; Zwiebach, B., Superstring theory on \(AdS_2 \times S^2\) as a coset supermanifold, Nucl. Phys. B, 567, 61 (2000) · Zbl 0951.81040
[23] Tseytlin, A. A., On a “universal” class of WZW type conformal models, Nucl. Phys. B, 418, 173 (1994) · Zbl 1009.81560
[24] Spiegelglas, M.; Yankielowicz, S., G/G topological field theories by cosetting G(k), Nucl. Phys. B, 393, 301 (1993) · Zbl 1245.81248
[25] Fateev, V. A.; Onofri, E.; Zamolodchikov, A. B., The Sausage model (integrable deformations of \(O(3)\) sigma model), Nucl. Phys. B, 406, 521 (1993) · Zbl 0990.81683
[26] Lukyanov, S. L., The integrable harmonic map problem versus Ricci flow, Nucl. Phys. B, 865, 308 (2012) · Zbl 1262.81145
[27] Grigoriev, M.; Tseytlin, A. A., Pohlmeyer reduction of \(AdS_5 \times S^5\) superstring sigma model, Nucl. Phys. B, 800, 450 (2008) · Zbl 1292.81114
[28] Hoare, B., Towards a two-parameter q-deformation of \(AdS_3 \times S^3 \times M^4\) superstrings, Nucl. Phys. B, 891, 259 (2015) · Zbl 1328.81178
[29] Lunin, O.; Roiban, R.; Tseytlin, A. A., Supergravity backgrounds for deformations of \(AdS_n \times S^n\) supercoset string models, Nucl. Phys. B, 891, 106 (2015) · Zbl 1328.81182
[30] Mikhailov, A.; Schafer-Nameki, S., Sine-Gordon-like action for the superstring in \(AdS_5 \times S^5\), J. High Energy Phys., 0805, 075 (2008)
[31] Grigoriev, M.; Tseytlin, A. A., On reduced models for superstrings on \(AdS_n \times S^n\), Int. J. Mod. Phys. A, 23, 2107 (2008) · Zbl 1146.81319
[32] Hull, C. M., Timelike T duality, de Sitter space, large N gauge theories and topological field theory, J. High Energy Phys., 9807, 021 (1998) · Zbl 0958.81085
[33] Arutyunov, G.; van Tongeren, S. J., \(AdS_5 \times S^5\) mirror model as a string sigma model, Phys. Rev. Lett., 113, 261605 (2014)
[34] Arutyunov, G.; van Tongeren, S. J., Double Wick rotating Green-Schwarz strings · Zbl 1388.81470
[35] Beisert, N.; Ricci, R.; Tseytlin, A. A.; Wolf, M., Dual superconformal symmetry from \(AdS_5 \times S^5\) superstring integrability, Phys. Rev. D, 78, 126004 (2008)
[36] Balog, J.; Forgacs, P.; Mohammedi, N.; Palla, L.; Schnittger, J., On quantum T duality in sigma models, Nucl. Phys. B, 535, 461 (1998) · Zbl 0956.81064
[37] Vicedo, B., Deformed integrable \(σ\)-models, classical \(R\)-matrices and classical exchange algebra on Drinfel’d doubles · Zbl 1422.37037
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