zbMATH — the first resource for mathematics

Abelian Yang-Baxter deformations and \(TsT\) transformations. (English) Zbl 1354.81048
Summary: We prove that abelian Yang-Baxter deformations of superstring coset \(\sigma\) models are equivalent to sequences of commuting \(TsT\) transformations, meaning \(T\) dualities and coordinate shifts. Our results extend also to fermionic deformations and fermionic \(T\) duality, and naturally lead to a \(TsT\) subgroup of the superduality group \(\operatorname{OSp}(d_b, d_b | 2 d_f)\). In cases like \(\mathrm{AdS}_5 \times \mathrm{S}^5\), fermionic deformations necessarily lead to complex models. As an illustration of inequivalent deformations, we give all six abelian deformations of \(\mathrm{AdS}_3\). We comment on the possible dual field theory interpretation of these (super-)\(TsT\) models.

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
14D15 Formal methods and deformations in algebraic geometry
22E70 Applications of Lie groups to the sciences; explicit representations
Full Text: DOI arXiv
[1] Maldacena, J. M., The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., Adv. Theor. Math. Phys., 2, 231-1133, (1998) · Zbl 0914.53047
[2] Arutyunov, G.; Frolov, S., Foundations of the \(A d S_5 \times S^5\) superstring: I, J. Phys. A, Math. Gen., 42, 254003, (June 2009)
[3] Beisert, N., Review of AdS/CFT integrability: an overview, Lett. Math. Phys., 99, 3-32, (2012)
[4] Bombardelli, D.; Cagnazzo, A.; Frassek, R.; Levkovich-Maslyuk, F.; Loebbert, F.; Negro, S.; Szécsényi, I. M.; Sfondrini, A.; van Tongeren, S. J.; Torrielli, A., An integrability primer for the gauge-gravity correspondence: an introduction, J. Phys. A, 49, 32, 320301, (2016) · Zbl 1344.00006
[5] Lunin, O.; Maldacena, J., Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, J. High Energy Phys., 5, (May 2005)
[6] Frolov, S.; Roiban, R.; Tseytlin, A. A., Gauge-string duality for superconformal deformations of \(N = 4\) super Yang-Mills theory, J. High Energy Phys., 0507, (2005) · Zbl 1114.81330
[7] Frolov, S., Lax pair for strings in lunin-Maldacena background, J. High Energy Phys., 5, (May 2005)
[8] Klimcik, C., Yang-Baxter sigma models and ds/AdS T duality, J. High Energy Phys., 0212, (2002)
[9] Klimčík, C., On integrability of the Yang-Baxter σ-model, J. Math. Phys., 50, (Apr. 2009)
[10] Delduc, F.; Magro, M.; Vicedo, B., On classical q-deformations of integrable σ-models, J. High Energy Phys., 11, (Nov. 2013)
[11] Delduc, F.; Magro, M.; Vicedo, B., Integrable deformation of the \(\text{AdS}_5 \times \text{S}^5\) superstring action, Phys. Rev. Lett., 112, (Feb. 2014)
[12] Sfetsos, K., Integrable interpolations: from exact CFTs to non-abelian T-duals, Nucl. Phys. B, 880, 225-246, (2014) · Zbl 1284.81257
[13] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., An integrable deformation of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring, J. Phys. A, 47, 49, 495402, (2014) · Zbl 1305.81120
[14] Demulder, S.; Sfetsos, K.; Thompson, D. C., Integrable λ-deformations: squashing coset CFTs and \(A d S_5 \times S^5\), J. High Energy Phys., 07, (2015) · Zbl 1388.83790
[15] Klimcik, C.; Severa, P., Dual nonabelian duality and the Drinfeld double, Phys. Lett. B, 351, 455-462, (1995)
[16] Klimcik, C., Poisson-Lie T duality, Nucl. Phys. B, Proc. Suppl., 46, 116-121, (1996) · Zbl 0957.81598
[17] Vicedo, B., Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles, J. Phys. A, 48, 35, 355203, (2015) · Zbl 1422.37037
[18] Hoare, B.; Tseytlin, A. A., On integrable deformations of superstring sigma models related to \(\text{AdS}_n \times \text{S}^n\) supercosets, Nucl. Phys. B, 897, 448-478, (2015) · Zbl 1329.81317
[19] Sfetsos, K.; Siampos, K.; Thompson, D. C., Generalised integrable λ- and η-deformations and their relation, Nucl. Phys. B, 899, 489-512, (2015) · Zbl 1331.81248
[20] Klimcik, C., η and λ deformations as \(\mathcal{E}\)-models, Nucl. Phys. B, 900, 259-272, (2015) · Zbl 1331.81182
[21] Delduc, F.; Lacroix, S.; Magro, M.; Vicedo, B., On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models · Zbl 1349.81128
[22] Borsato, R.; Tseytlin, A. A.; Wulff, L., Supergravity background of λ-deformed model for \(\text{AdS}_2 \times \text{S}^2\) supercoset, Nucl. Phys. B, 905, 264-292, (2016) · Zbl 1332.81170
[23] Chervonyi, Y.; Lunin, O., Supergravity background of the λ-deformed \(\text{AdS}_3 \times \text{S}^3\) supercoset, Nucl. Phys. B, 910, 685-711, (2016) · Zbl 1345.83040
[24] Chervonyi, Y.; Lunin, O., Generalized λ-deformations of \(A d S_p \times S^p\) · Zbl 1349.81150
[25] Kawaguchi, I.; Matsumoto, T.; Yoshida, K., Jordanian deformations of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring, J. High Energy Phys., 1404, (2014)
[26] Delduc, F.; Magro, M.; Vicedo, B., Derivation of the action and symmetries of the q-deformed \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring, J. High Energy Phys., 1410, (2014) · Zbl 1333.81322
[27] van Tongeren, S. J., Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory, Nucl. Phys. B, 904, 148-175, (2016) · Zbl 1332.81197
[28] Borsato, R.; Wulff, L., Target space supergeometry of η and λ-deformed strings · Zbl 1390.81412
[29] Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, A. A., Scale invariance of the η-deformed \(A d S_5 \times S^5\) superstring, T-duality and modified type II equations, Nucl. Phys. B, 903, 262-303, (2016) · Zbl 1332.81167
[30] Wulff, L.; Tseytlin, A. A., Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations, J. High Energy Phys., 06, (2016) · Zbl 1390.83426
[31] Arutyunov, G.; Borsato, R.; Frolov, S., Puzzles of η-deformed \(\text{AdS}_5 \times \text{S}^5\), J. High Energy Phys., 12, (Dec. 2015)
[32] Hoare, B.; Tseytlin, A. A., Type IIB supergravity solution for the T-dual of the η-deformed \(\text{AdS}_5 \times \text{S}^5\) superstring, J. High Energy Phys., 10, (2015) · Zbl 1388.83824
[33] Hoare, B.; van Tongeren, S. J., Non-split and split deformations of \(A d S_5\) · Zbl 1354.81047
[34] Arutyunov, G.; de Leeuw, M.; van Tongeren, S. J., The exact spectrum and mirror duality of the \((\operatorname{AdS}_5 \times \operatorname{S}^5)_\eta\) superstring, Theor. Math. Phys., 182, 1, 23-51, (2015) · Zbl 1317.81211
[35] Arutyunov, G.; van Tongeren, S. J., The \(\operatorname{AdS}_5 \times \operatorname{S}^5\) mirror model as a string, Phys. Rev. Lett., 113, (2014)
[36] Arutyunov, G.; van Tongeren, S. J., Double Wick rotating Green-Schwarz strings, J. High Energy Phys., 1505, (2015) · Zbl 1388.81470
[37] Pachoł, A.; van Tongeren, S. J., Quantum deformations of the flat space superstring, Phys. Rev. D, 93, (2016)
[38] Hoare, B.; van Tongeren, S. J., On Jordanian deformations of \(A d S_5\) and supergravity · Zbl 1352.81050
[39] Kyono, H.; Yoshida, K., Supercoset construction of Yang-Baxter deformed \(A d S_5 \times S^5\) backgrounds, ArXiv e-prints, May 2016
[40] Orlando, D.; Reffert, S.; Sakamoto, J.-i.; Yoshida, K., Generalized type IIB supergravity equations and non-abelian classical r-matrices · Zbl 1354.83054
[41] Matsumoto, T.; Yoshida, K., Integrability of classical strings dual for noncommutative gauge theories, J. High Energy Phys., 1406, (2014) · Zbl 1333.81262
[42] Matsumoto, T.; Yoshida, K., Integrable deformations of the \(\text{AdS}_5 \times \text{S}^5\) superstring and the classical Yang-Baxter equation - towards the gravity/CYBE correspondence, J. Phys. Conf. Ser., 563, (Nov. 2014)
[43] Tongeren, S. J.v., On classical Yang-Baxter based deformations of the \(\text{AdS}_5 \times \text{S}^5\) superstring, J. High Energy Phys., 6, (June 2015)
[44] Matsumoto, T.; Yoshida, K., Towards the gravity/CYBE correspondence - the current status, J. Phys. Conf. Ser., 670, 1, (2016)
[45] Matsumoto, T.; Yoshida, K., Lunin-Maldacena backgrounds from the classical Yang-Baxter equation - towards the gravity/CYBE correspondence, J. High Energy Phys., 1406, (2014) · Zbl 1333.83196
[46] Metsaev, R. R.; Tseytlin, A. A., Type IIB superstring action in \(\text{AdS}_5 \times \text{S}^5\) background, Nucl. Phys. B, 533, 109-126, (Nov. 1998)
[47] Buscher, T. H., A symmetry of the string background field equations, Phys. Lett. B, 194, 59-62, (July 1987)
[48] Berkovits, N.; Maldacena, J., Dual superconformal symmetry, and the amplitude/Wilson loop connection, J. High Energy Phys., 9, (Sept. 2008)
[49] Beisert, N.; Ricci, R.; Tseytlin, A. A.; Wolf, M., Dual superconformal symmetry from \(A d S_5 \times S^5\) superstring integrability, Phys. Rev. D, 78, (Dec. 2008)
[50] Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Phys. Rep., 244, 77-202, (Aug. 1994)
[51] Alday, L. F.; Arutyunov, G.; Frolov, S., Green-Schwarz strings in tst-transformed backgrounds, J. High Energy Phys., 06, (2006)
[52] Siegel, W., Superspace duality in low-energy superstrings, Phys. Rev. D, 48, 2826-2837, (1993)
[53] Fre, P.; Grassi, P. A.; Sommovigo, L.; Trigiante, M., Theory of superdualities and the orthosymplectic supergroup, Nucl. Phys. B, 825, 177-202, (2010) · Zbl 1196.81164
[54] Bergshoeff, E.; Hull, C.; Ortín, T., Duality in the type-II superstring effective action, Nucl. Phys. B, 451, 547-575, (Oct. 1995)
[55] Kulik, B.; Roiban, R., T-duality of the Green-Schwarz superstring, J. High Energy Phys., 9, (Sept. 2002)
[56] Hassan, S. F., T-duality, space-time spinors and R-R fields in curved backgrounds, Nucl. Phys. B, 568, 145-161, (Mar. 2000)
[57] Fukuma, M.; Oota, T.; Tanaka, H., Comments on T-dualities of Ramond-Ramond potentials, Prog. Theor. Phys., 103, 425-446, (Feb. 2000)
[58] Brace, D.; Morariu, B.; Zumino, B., T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B, 549, 181-193, (May 1999)
[59] Hassan, S. F., \(S O(d, d)\) transformations of Ramond-Ramond fields and space-time spinors, Nucl. Phys. B, 583, 431-453, (2000) · Zbl 0984.81117
[60] Sfetsos, K.; Siampos, K.; Thompson, D. C., Canonical pure spinor (fermionic) T-duality, Class. Quantum Gravity, 28, (2011) · Zbl 1210.83043
[61] Hoare, B., Towards a two-parameter q-deformation of \(A d S_3 \times S^3 \times M^4\) superstrings, Nucl. Phys. B, 891, 259-295, (2015) · Zbl 1328.81178
[62] Patera, J.; Winternitz, P.; Zassenhaus, H., Continuous subgroups of the fundamental groups of physics. I. general method and the Poincaré group, J. Math. Phys., 16, 8, (1975) · Zbl 0314.22007
[63] Hashimoto, A.; Itzhaki, N., Noncommutative Yang-Mills and the AdS/CFT correspondence, Phys. Lett. B, 465, 142-147, (1999) · Zbl 0987.81108
[64] Maldacena, J. M.; Russo, J. G., Large N limit of noncommutative gauge theories, J. High Energy Phys., 9909, (1999) · Zbl 0957.81083
[65] Fokken, J.; Sieg, C.; Wilhelm, M., Non-conformality of \(\gamma_i\)-deformed \(N = 4\) SYM theory, J. Phys. A, 47, 455401, (2014) · Zbl 1304.81122
[66] van Tongeren, S. J., Integrability of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring and its deformations, J. Phys. A, 47, 43, 433001, (2014) · Zbl 1319.81071
[67] Fokken, J.; Sieg, C.; Wilhelm, M., A piece of cake: the ground-state energies in \(\gamma_i\)-deformed \(\mathcal{N} = 4\) SYM theory at leading wrapping order, J. High Energy Phys., 1409, (2014)
[68] Arutyunov, G.; Medina-Rincon, D., Deformed Neumann model from spinning strings on \((A d S_5 \times S^5)_\eta\), J. High Energy Phys., 10, (2014)
[69] Banerjee, A.; Panigrahi, K. L., On the rotating and oscillating strings in \((\text{AdS}_3 \times \text{S}^3)_\kappa\), J. High Energy Phys., 09, (2014)
[70] Kameyama, T.; Yoshida, K., A new coordinate system for q-deformed \(\text{Ad}_5 \times \text{S}^5\) and classical string solutions, J. Phys. A, 48, 7, (2015)
[71] Arutyunov, G.; Heinze, M.; Medina-Rincon, D., Integrability of the eta-deformed Neumann-Rosochatius model · Zbl 1357.81135
[72] Banerjee, A.; Panigrahi, K. L., On circular strings in \((A d S_3 \times S^3)_ϰ\)
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.