×

zbMATH — the first resource for mathematics

Integrable interpolations: From exact CFTs to non-abelian T-duals. (English) Zbl 1284.81257
Summary: We derive two new classes of integrable theories interpolating between exact CFT WZW or gauged WZW models and non-abelian T-duals of principal chiral models or geometric coset models. They are naturally constructed by gauging symmetries of integrable models. Our analysis implies that non-abelian T-duality preserves integrability and suggests a novel way to understand the global properties of the corresponding backgrounds.

MSC:
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Rajeev, S. G., Nonabelian bosonization without Wess-Zumino terms. 1. new current algebra, Phys. Lett. B, 217, 123, (1989)
[2] 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)
[3] Evans, J. M.; Hollowood, T. J., Integrable theories that are asymptotically CFT, Nucl. Phys. B, 438, 469, (1995) · Zbl 1052.81605
[4] Sfetsos, K., Gauged WZW models and non-abelian duality, Phys. Rev. D, 50, 2784, (1994)
[5] Polychronakos, A. P.; Sfetsos, K., High spin limits and non-abelian T-duality, Nucl. Phys. B, 843, 344, (2011) · Zbl 1207.81133
[6] Fateev, V. A.; Zamolodchikov, A. B., Integrable perturbations of \(Z(N)\) parafermion models and \(O(3)\) sigma model, Phys. Lett. B, 271, 91, (1991)
[7] Fridling, B. E.; Jevicki, A., Dual representations and ultraviolet divergences in nonlinear σ models, Phys. Lett. B, 134, 70, (1984)
[8] Fradkin, E. S.; Tseytlin, A. A., Quantum equivalence of dual field theories, Ann. Phys., 162, 31, (1985)
[9] de la Ossa, X. C.; Quevedo, F., Duality symmetries from non-abelian isometries in string theory, Nucl. Phys. B, 403, 377, (1993) · Zbl 1030.81513
[10] Sfetsos, K.; Thompson, D. C., On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys. B, 846, (2011) · Zbl 1208.81173
[11] Lozano, Y.; O’Colgain, E.; Sfetsos, K.; Thompson, D. C., Non-abelian T-duality, Ramond fields and coset geometries, J. High Energy Phys., 1106, 106, (2011) · Zbl 1298.81316
[12] Itsios, G.; Nunez, C.; Sfetsos, K.; Thompson, D. C., Non-abelian T-duality and the AdS/CFT correspondence: new \(\mathcal{N} = 1\) backgrounds, Nucl. Phys. B, 873, 1, (2013) · Zbl 1282.81147
[13] de Boer, J.; Halpern, M. B., Unified Einstein-Virasoro master equation in the general nonlinear sigma model, Int. J. Mod. Phys. A, 12, 1551, (1997) · Zbl 0985.81737
[14] Bardakci, K.; Halpern, M. B.; Halpern, M. B.; Goddard, P.; Kent, A.; Olive, D. I., Virasoro algebras and coset space models, Phys. Rev. D, Phys. Rev. D, Phys. Lett. B, 152, 88, (1985) · Zbl 0661.17015
[15] Karabali, D.; Park, Q. H.; Schnitzer, H. J.; Yang, Z.; Karabali, D.; Schnitzer, H. J.; Gawedzki, K.; Kupiainen, A., \(G / H\) conformal field theory from gauged WZW model, Phys. Lett. B, Nucl. Phys. B, Phys. Lett. B, 215, 119, (1988)
[16] Polyakov, A. M.; Pohlmeyer, K.; Luscher, M.; Luscher, M.; Pohlmeyer, K., Scattering of massless lumps and nonlocal charges in the two-dimensional classical nonlinear sigma model, Phys. Lett. B, Commun. Math. Phys., Nucl. Phys. B, Nucl. Phys. B, 137, 46, (1978)
[17] Kadanoff, L. P.; Brown, A. C., Correlation functions on the critical lines of the Baxter and ashkin-Teller models, Ann. Phys., 121, 318, (1979)
[18] Chaudhuri, S.; Schwartz, J. A., A criterion for integrably marginal operators, Phys. Lett. B, 219, 291, (1989)
[19] Tseytlin, A. A., On a ‘universal’ class of WZW type conformal models, Nucl. Phys. B, 418, 173, (1994) · Zbl 1009.81560
[20] Klimcik, C., On integrability of the Yang-Baxter sigma-model, J. Math. Phys., 50, 043508, (2009) · Zbl 1215.81099
[21] Sfetsos, K., Duality invariant class of two-dimensional field theories, Nucl. Phys. B, 561, 316, (1999) · Zbl 0958.81156
[22] Bardacki, K.; Crescimanno, M. J.; Rabinovici, E., Parafermions from coset models, Nucl. Phys. B, 344, 344, (1990)
[23] Bardakci, K.; Crescimanno, M. J.; Hotes, S., Parafermions from nonabelian coset models, Nucl. Phys. B, 349, 439, (1991)
[24] Fateev, V. A.; Zamolodchikov, A. B., Parafermionic currents in the two-dimensional conformal quantum field theory and selfdual critical points in \(Z(n)\) invariant statistical systems, Sov. Phys. JETP, Zh. Eksp. Teor. Fiz., 89, 380, (1985)
[25] Petropoulos, P. M.; Sfetsos, K., NS5-branes on an ellipsis and novel marginal deformations with parafermions, J. High Energy Phys., 0601, 167, (2006)
[26] Petropoulos, P. M.; Sfetsos, K., Non-abelian coset string backgrounds from asymptotic and initial data, J. High Energy Phys., 0704, 033, (2007)
[27] Fotopoulos, A.; Petropoulos, P. M.; Prezas, N.; Sfetsos, K., Holographic approach to deformations of NS5-brane distributions and exact cfts, J. High Energy Phys., 0802, 087, (2008)
[28] Cherednik, I. V., Relativistically invariant quasiclassical limits of integrable two-dimensional quantum models, Theor. Math. Phys., Teor. Mat. Fiz., 47, 225, (1981)
[29] Mohammedi, N., On the geometry of classically integrable two-dimensional non-linear sigma models, Nucl. Phys. B, 839, 420, (2010) · Zbl 1206.37038
[30] Itsios, G.; Nunez, C.; Sfetsos, K.; Thompson, D. C., On non-abelian T-duality and new \(\mathcal{N} = 1\) backgrounds, Phys. Lett. B, 721, 342, (2013) · Zbl 1309.83091
[31] Lozano, Y.; O Colgain, E.; Rodriguez-Gomez, D.; Sfetsos, K., New supersymmetric \(\mathit{AdS}_6\) via T-duality, Phys. Rev. Lett., 110, 231601, (2013)
[32] Barranco, A.; Gaillard, J.; Macpherson, N. T.; Nunez, C.; Thompson, D. C., G-structures and flavouring non-abelian T-duality, J. High Energy Phys., 1308, 018, (2013)
[33] Lozano, Y.; O Colgain, E.; Rodriguez-Gomez, D., Hints of 5d fixed point theories from non-abelian T-duality · Zbl 1333.83249
[34] Delduc, F.; Magro, M.; Vicedo, B., An integrable deformation of the \(\mathit{AdS}_5 \times S^5\) superstring action · Zbl 1333.81322
[35] Hoare, B.; Hollowood, T. J.; Miramontes, J. L., q-deformation of the \(\mathit{AdS}_5 \times S^5\) superstring S-matrix and its relativistic limit, J. High Energy Phys., 1203, 015, (2012) · Zbl 1309.81186
[36] Arutyunov, G.; Borsato, R.; Frolov, S., S-matrix for strings on η-deformed \(\mathit{AdS}_5 \times S_5\)
[37] Drinfeld, V. G., Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl., Dokl. Akad. Nauk SSSR, Ser. Fiz., 283, 1060, (1985)
[38] Bernard, D., An introduction to Yangian symmetries, Int. J. Mod. Phys. B, 7, 3517, (1993) · Zbl 0805.35102
[39] Torrielli, A., Review of AdS/CFT integrability, chapter VI.2: Yangian algebra, Lett. Math. Phys., 99, 547, (2012) · Zbl 1243.81183
[40] MacKay, N. J.; MacKay, N. J., On the classical origins of Yangian symmetry in integrable field theory, Phys. Lett. B, Phys. Lett. B, 308, 444, (1993), (Erratum)
[41] Abdalla, E.; Abdalla, M. C.B.; Forger, M., Exact S-matrices for anomaly free nonlinear σ-models on symmetric spaces, Nucl. Phys. B, 297, 374, (1988)
[42] Evans, J. M.; Hassan, M.; MacKay, N. J.; Mountain, A. J., Local conserved charges in principal chiral models, Nucl. Phys. B, 561, 385, (1999) · Zbl 0958.81028
[43] Kawaguchi, I.; Yoshida, K.; Kawaguchi, I.; Orlando, D.; Yoshida, K., Yangian symmetry in deformed WZNW models on squashed spheres, J. High Energy Phys., Phys. Lett. B, 701, 475, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.