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Generalised integrable \(\lambda\)- and \(\eta\)-deformations and their relation. (English) Zbl 1331.81248
Summary: We construct two-parameter families of integrable \(\lambda\)-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric coset space. In examples based on the \(\operatorname{SU}(2)\) WZW model and the \(\operatorname{SU}(2) / \operatorname{U}(1)\) exact coset CFT, we show that these deformations are related to bi-Yang-Baxter generalisations of \(\eta\)-deformations via Poisson-Lie T-duality and analytic continuation. We illustrate the quantum behaviour of our models under RG flow. As a byproduct we demonstrate that the bi-Yang-Baxter \(\sigma\)-model for a general group is one-loop renormalisable.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
14D15 Formal methods and deformations in algebraic geometry
81T17 Renormalization group methods applied to problems in quantum field theory
81T18 Feynman diagrams
16T25 Yang-Baxter equations
22E70 Applications of Lie groups to the sciences; explicit representations
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References:
[1] Minahan, J. A.; Zarembo, K., The Bethe ansatz for \(\mathcal{N} = 4\) super Yang-Mills, J. High Energy Phys., 0303, (2003)
[2] Metsaev, R. R.; Tseytlin, A. A., Type IIB superstring action in \(\mathit{AdS}_5 \times S^5\) background, Nucl. Phys. B, 533, 109, (1998) · Zbl 0956.81063
[3] Bena, I.; Polchinski, J.; Roiban, R., Hidden symmetries of the \(\mathit{AdS}_5 \times S^5\) superstring, Phys. Rev. D, 69, (2004)
[4] Delduc, F.; Magro, M.; Vicedo, B., On classical q-deformations of integrable sigma-models, J. High Energy Phys., 1311, (2013) · Zbl 1342.81182
[5] Delduc, F.; Magro, M.; Vicedo, B., An integrable deformation of the \(\mathit{AdS}_5 \times S^5\) superstring action, Phys. Rev. Lett., 112, 5, (2014) · Zbl 1333.81322
[6] Klimčík, C., YB sigma models and ds/AdS T duality, J. High Energy Phys., 0212, (2002)
[7] Klimčík, C., On integrability of the YB sigma-model, J. Math. Phys., 50, (2009)
[8] Arutyunov, G.; Borsato, R.; Frolov, S., S-matrix for strings on η-deformed \(\mathit{AdS}_5 \times S^5\), J. High Energy Phys., 1404, (2014)
[9] Sfetsos, K., Integrable interpolations: from exact CFTs to non-abelian T-duals, Nucl. Phys. B, 880, 225, (2014) · Zbl 1284.81257
[10] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., Integrable deformations of strings on symmetric spaces, J. High Energy Phys., 1411, (2014) · Zbl 1333.81341
[11] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D., An integrable deformation of the \(\mathit{AdS}_5 \times S^5\) superstring, J. Phys. A, 47, 49, 495402, (2014) · Zbl 1305.81120
[12] Rajeev, S. G., Nonabelian bosonization without Wess-Zumino terms. 1. new current algebra, Phys. Lett. B, 217, 123, (1989)
[13] Balog, J.; Forgacs, P.; Horvath, Z.; Palla, L., A new family of \(\mathit{SU}(2)\) symmetric integrable sigma models, Phys. Lett. B, 324, 403, (1994)
[14] Klimčík, C.; Ševera, P., Dual non-abelian duality and the Drinfeld double, Phys. Lett. B, 351, 455, (1995)
[15] Klimčík, C.; Ševera, P., Poisson-Lie T-duality and loop groups of Drinfeld doubles, Phys. Lett. B, 372, 65, (1996) · Zbl 1037.81576
[16] Sfetsos, K., Poisson-Lie T duality and supersymmetry, Nucl. Phys. B, Proc. Suppl., 56, 302, (1997) · Zbl 0957.81635
[17] Sfetsos, K., Canonical equivalence of nonisometric sigma models and Poisson-Lie T duality, Nucl. Phys. B, 517, 549, (1998) · Zbl 0945.81022
[18] Vicedo, B., Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles · Zbl 1422.37037
[19] Hoare, B.; Tseytlin, A. A., On integrable deformations of superstring sigma models related to \(\mathit{AdS}_n \times S^n\) supercosets, Nucl. Phys. B, 897, 448, (2015) · Zbl 1329.81317
[20] Klimčík, C., Integrability of the bi-Yang-Baxter sigma-model, Lett. Math. Phys., 104, 1095, (2014) · Zbl 1359.70102
[21] Sfetsos, K.; Siampos, K., The anisotropic λ-deformed \(\mathit{SU}(2)\) model is integrable, Phys. Lett. B, 743, 160, (2015) · Zbl 1343.81131
[22] Babelon, O.; Bernard, D.; Talon, M., Introduction to classical integrable systems, (2003), Cambridge University Press · Zbl 1045.37033
[23] Kawaguchi, I.; Matsumoto, T.; Yoshida, K., Jordanian deformations of the \(\mathit{AdS}_5 \times S^5\) superstring, J. High Energy Phys., 1404, (2014)
[24] Matsumoto, T.; Yoshida, K., Integrability of classical strings dual for noncommutative gauge theories, J. High Energy Phys., 1406, (2014) · Zbl 1333.81262
[25] Matsumoto, T.; Yoshida, K., Schrödinger geometries arising from Yang-Baxter deformations, J. High Energy Phys., 1504, (2015) · Zbl 1388.83866
[26] van Tongeren, S. J., On classical YB based deformations of the \(\mathit{AdS}_5 \times S^5\) superstring, J. High Energy Phys., 1506, (2015)
[27] van Tongeren, S. J., YB deformations, AdS/CFT, and twist-noncommutative gauge theory · Zbl 1332.81197
[28] Valent, G.; Klimčík, C.; Squellari, R., One loop renormalizability of the Poisson-Lie sigma models, Phys. Lett. B, 678, 143, (2009)
[29] Sfetsos, K., Duality invariant class of two-dimensional field theories, Nucl. Phys. B, 561, 316, (1999) · Zbl 0958.81156
[30] Sfetsos, K.; Siampos, K., Quantum equivalence in Poisson-Lie T-duality, J. High Energy Phys., 0906, (2009)
[31] Sfetsos, K.; Siampos, K.; Thompson, D. C., Renormalization of Lorentz non-invariant actions and manifest T-duality, Nucl. Phys. B, 827, 545, (2010) · Zbl 1203.81151
[32] Squellari, R., Yang-Baxter σ model: quantum aspects, Nucl. Phys. B, 881, 502, (2014) · Zbl 1284.81194
[33] Itsios, G.; Sfetsos, K.; Siampos, K.; Torrielli, A., The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories, Nucl. Phys. B, 889, 64, (2014) · Zbl 1326.81180
[34] Hoare, B.; Roiban, R.; Tseytlin, A. A., On deformations of \(\mathit{AdS}_n \times S^n\) supercosets, J. High Energy Phys., 1406, (2014)
[35] Fateev, V. A., The sigma model (dual) representation for a two-parameter family of integrable quantum field theories, Nucl. Phys. B, 473, 509, (1996) · Zbl 0925.81297
[36] Sfetsos, K.; Thompson, D. C., Spacetimes for λ-deformations, J. High Energy Phys., 1412, (2014)
[37] Demulder, S.; Sfetsos, K.; Thompson, D. C., Integrable λ-deformations: squashing coset CFTs and \(\mathit{AdS}_5 \times S^5\), J. High Energy Phys., (2015), in press · Zbl 1388.83790
[38] Klimčík, C.; Severa, P., Dressing cosets, Phys. Lett. B, 381, 56, (1996) · Zbl 0979.81512
[39] Ecker, G.; Honerkamp, J.; Honerkamp, J., Chiral multiloops, Nucl. Phys. B, Nucl. Phys. B, 36, 130, (1972)
[40] Friedan, D.; Friedan, D., Nonlinear models in two + epsilon dimensions, Phys. Rev. Lett., Ann. Phys., 163, 318, (1985) · Zbl 0583.58010
[41] Curtright, T. L.; Zachos, C. K.; Braaten, E.; Curtright, T. L.; Zachos, C. K.; Fridling, B. E.; van de Ven, A. E.M., Renormalization of generalized two-dimensional nonlinear σ-models, Phys. Rev. Lett., Nucl. Phys. B, Nucl. Phys. B, 268, 719, (1986)
[42] Squellari, R., Dressing cosets revisited, Nucl. Phys. B, 853, 379, (2011) · Zbl 1229.81258
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