van Tongeren, Stijn J. Almost abelian twists and AdS/CFT. (English) Zbl 1369.81081 Phys. Lett., B 765, 344-351 (2017). Summary: A large class of the recently found unimodular nonabelian homogeneous Yang-Baxter deformations of the \(\operatorname{AdS}_5 \times \operatorname{S}^5\) superstring can be realized as sequences of noncommuting TsT transformations. I show that many of them are duals to various noncommutative versions of supersymmetric Yang-Mills theory, structurally determined directly in terms of the associated \(r\) matrices, in line with previous expectations in the literature. Cited in 36 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T75 Noncommutative geometry methods in quantum field theory 16T25 Yang-Baxter equations Keywords:holography; AdS/CFT correspondence; integrability; noncommutative field theory; T duality PDFBibTeX XMLCite \textit{S. J. van Tongeren}, Phys. Lett., B 765, 344--351 (2017; Zbl 1369.81081) Full Text: DOI arXiv References: [1] Maldacena, J. M., The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.. Int. J. Theor. Phys., Adv. Theor. Math. Phys., 2, 231-1133 (1998) · Zbl 0914.53047 [2] Arutyunov, G.; Frolov, S., Foundations of the \(AdS_5 \times S^5\) superstring. Part I, J. Phys. A, 42, 254003 (2009) · Zbl 1167.81028 [3] Beisert, N.; Ahn, C.; Alday, L. F.; Bajnok, Z.; Drummond, J. M., 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, 320301 (2016) · Zbl 1344.00006 [5] Lunin, O.; Maldacena, J. M., Deforming field theories with \(U(1) \times U(1)\) global symmetry and their gravity duals, J. High Energy Phys., 0505, Article 033 pp. (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, Article 045 pp. (2005) · Zbl 1114.81330 [7] Frolov, S., Lax pair for strings in Lunin-Maldacena background, J. High Energy Phys., 0505, Article 069 pp. (2005) [8] Klimcik, C., Yang-Baxter sigma models and dS/AdS T duality, J. High Energy Phys., 0212, Article 051 pp. (2002) [9] Klimcik, C., On integrability of the Yang-Baxter sigma-model, J. Math. Phys., 50, Article 043508 pp. (2009) · Zbl 1215.81099 [10] Delduc, F.; Magro, M.; Vicedo, B., An integrable deformation of the \(AdS_5 \times S^5\) superstring action, Phys. Rev. Lett., 112, Article 051601 pp. (2014) · Zbl 1333.81322 [11] Sfetsos, K., Integrable interpolations: from exact CFTs to non-Abelian T-duals, Nucl. Phys. B, 880, 225-246 (2014) · Zbl 1284.81257 [12] 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 [13] 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, Article 019 pp. (2015) · Zbl 1388.83790 [14] 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, Article 132 pp. (2014) · Zbl 1333.81322 [15] Kawaguchi, I.; Matsumoto, T.; Yoshida, K., Jordanian deformations of the \(AdS_5 \times S^5\) superstring, J. High Energy Phys., 1404, Article 153 pp. (2014) [16] van Tongeren, S. J., Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory, Nucl. Phys. B, 904, 148-175 (2016) · Zbl 1332.81197 [17] Borsato, R.; Wulff, L., Target space supergeometry of \(η\) and \(λ\)-deformed strings, J. High Energy Phys., 10, Article 045 pp. (2016) · Zbl 1390.81412 [18] Arutyunov, G.; Borsato, R.; Frolov, S., Puzzles of \(η\)-deformed \(AdS_5 \times S^5\), J. High Energy Phys., 12, Article 049 pp. (2015) [19] Hoare, B.; van Tongeren, S. J., Non-split and split deformations of \(AdS_5\), J. Phys. A, 49, 48, 484003 (2016) · Zbl 1354.81047 [20] van Tongeren, S. J., On classical Yang-Baxter based deformations of the \(AdS_5 \times S^5\) superstring, J. High Energy Phys., 06, Article 048 pp. (2015) [21] Osten, D.; van Tongeren, S. J., Abelian Yang-Baxter deformations and TsT transformations (2016) · Zbl 1354.81048 [22] Kyono, H.; Yoshida, K., Supercoset construction of Yang-Baxter deformed \(AdS_5 \times S^5\) backgrounds, Prog. Theor. Exp. Phys., 03, Article 083 pp. (2016) [23] Hoare, B.; van Tongeren, S. J., On Jordanian deformations of \(AdS_5\) and supergravity, J. Phys. A, 49, 43, 434006 (2016) · Zbl 1352.81050 [24] Orlando, D.; Reffert, S.; Sakamoto, J.-i.; Yoshida, K., Generalized type IIB supergravity equations and non-Abelian classical r-matrices, J. Phys. A, 49, 44, 445403 (2016) · Zbl 1354.83054 [25] Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, A. A., Scale invariance of the \(η\)-deformed \(AdS_5 \times S^5\) superstring, T-duality and modified type II equations, Nucl. Phys. B, 903, 262-303 (2016) · Zbl 1332.81167 [26] Wulff, L.; Tseytlin, A. A., Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations · Zbl 1390.83426 [27] Hoare, B.; Tseytlin, A. A., Homogeneous Yang-Baxter deformations as non-abelian duals of the \(AdS_5\) sigma-model, J. Phys. A, 49, 49, 494001 (2016) · Zbl 1357.81149 [28] Borsato, R.; Wulff, L., Integrable deformations of T-dual \(σ\) models · Zbl 1332.81170 [29] Hashimoto, A.; Itzhaki, N., Noncommutative Yang-Mills and the AdS/CFT correspondence, Phys. Lett. B, 465, 142-147 (1999) · Zbl 0987.81108 [30] Maldacena, J. M.; Russo, J. G., Large N limit of noncommutative gauge theories, J. High Energy Phys., 9909, Article 025 pp. (1999) · Zbl 0957.81083 [31] Matsumoto, T.; Yoshida, K., Lunin-Maldacena backgrounds from the classical Yang-Baxter equation - towards the gravity/CYBE correspondence, J. High Energy Phys., 1406, Article 135 pp. (2014) · Zbl 1333.83196 [32] Matsumoto, T.; Yoshida, K., Integrability of classical strings dual for noncommutative gauge theories, J. High Energy Phys., 1406, Article 163 pp. (2014) · Zbl 1333.81262 [33] Schomerus, V., D-branes and deformation quantization, J. High Energy Phys., 9906, Article 030 pp. (1999) · Zbl 0961.81066 [34] Seiberg, N.; Witten, E., String theory and noncommutative geometry, J. High Energy Phys., 9909, Article 032 pp. (1999) · Zbl 0957.81085 [35] Seiberg, N.; Susskind, L.; Toumbas, N., Strings in background electric field, space/time noncommutativity and a new noncritical string theory, J. High Energy Phys., 0006, Article 021 pp. (2000) · Zbl 0989.81608 [36] Dasgupta, K.; Sheikh-Jabbari, M., Noncommutative dipole field theories, J. High Energy Phys., 0202, Article 002 pp. (2002) [37] Metsaev, R.; Tseytlin, A. A., Type IIB superstring action in \(AdS(5) \times S^5\) background, Nucl. Phys. B, 533, 109-126 (1998) · Zbl 0956.81063 [38] Ovando, G., Four dimensional symplectic Lie algebras, Beitr. Algebra Geom., 47, 419 (2006) · Zbl 1155.53042 [39] Borowiec, A.; Lukierski, J.; Tolstoy, V. N., New twisted quantum deformations of \(D = 4\) super-Poincare algebra (2008), in: Proceedings, 7th International Workshop on Supersymmetries and Quantum Symmetries (SQS’07): Dubna, Russia, July 30-August 04, 2007 · Zbl 1189.81101 [40] Szabo, R. J., Symmetry, gravity and noncommutativity, Class. Quantum Gravity, 23, R199-R242 (2006) · Zbl 1117.83001 [41] Dimitrijevic, M.; Jonke, L.; Pachoł, A., Gauge theory on twisted \(κ\)-Minkowski: old problems and possible solutions, SIGMA, 10, Article 063 pp. (2014) · Zbl 1295.81125 [42] Cornalba, L.; Schiappa, R., Nonassociative star product deformations for D-brane world volumes in curved backgrounds, Commun. Math. Phys., 225, 33-66 (2002) · Zbl 1042.81065 [43] Kontsevich, M., Deformation quantization of Poisson manifolds. 1, Lett. Math. Phys., 66, 157-216 (2003) · Zbl 1058.53065 [44] Gopakumar, R.; Maldacena, J. M.; Minwalla, S.; Strominger, A., S duality and noncommutative gauge theory, J. High Energy Phys., 0006, Article 036 pp. (2000) · Zbl 0989.81125 [45] Aharony, O.; Gomis, J.; Mehen, T., On theories with lightlike noncommutativity, J. High Energy Phys., 0009, Article 023 pp. (2000) · Zbl 0989.81621 [46] Hashimoto, A.; Thomas, K., Non-commutative gauge theory on D-branes in Melvin universes, J. High Energy Phys., 0601, Article 083 pp. (2006) [47] 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 [48] Fokken, J.; Sieg, C.; Wilhelm, M., A piece of cake: the ground-state energies in \(\gamma_i\)-deformed \(N = 4\) SYM theory at leading wrapping order, J. High Energy Phys., 1409, Article 78 pp. (2014) [49] van Tongeren, S. J., Integrability of the \(AdS_5 \times S^5\) superstring and its deformations, J. Phys. A, 47, 43, 433001 (2014) · Zbl 1319.81071 [50] Dhokarh, D.; Haque, S. S.; Hashimoto, A., Melvin twists of global \(AdS(5) \times S(5)\) and their non-commutative field theory dual, J. High Energy Phys., 08, Article 084 pp. (2008) [51] Pachoł, A.; van Tongeren, S. J., Quantum deformations of the flat space superstring, Phys. Rev. D, 93, Article 026008 pp. (2016) [52] Arutyunov, G.; van Tongeren, S. J., The \(AdS_5 \times S^5\) mirror model as a string, Phys. Rev. Lett., 113, Article 261605 pp. (2014) [53] Arutyunov, G.; van Tongeren, S. J., Double Wick rotating Green-Schwarz strings, J. High Energy Phys., 1505, Article 027 pp. (2015) · Zbl 1388.81470 [54] Borowiec, A.; Kyono, H.; Lukierski, J.; Sakamoto, J.-i.; Yoshida, K., Yang-Baxter sigma models and Lax pairs arising from \(κ\)-Poincaré \(r\)-matrices, J. High Energy Phys., 04, Article 079 pp. (2016) · Zbl 1388.81032 [55] Hoare, B.; Tseytlin, A. A., Type IIB supergravity solution for the T-dual of the \(η\)-deformed \(AdS_5 \times S^5\) superstring, J. High Energy Phys., 10, Article 060 pp. (2015) · Zbl 1388.83824 [56] Arutyunov, G.; de Leeuw, M.; van Tongeren, S. J., The exact spectrum and mirror duality of the \((AdS_5 \times S^5)_\eta\) superstring, Theor. Math. Phys., 182, 1, 23-51 (2015) · Zbl 1317.81211 [57] Drinfeld, V., On constant quasi-classical solutions of the Yang-Baxter quantum equation, Sov. Math. Dokl., 28, 667 (1983) [58] Reshetikhin, N., Multiparameter quantum groups and twisted quasitriangular Hopf algebras, Lett. Math. Phys., 20, 331-335 (1990) · Zbl 0719.17006 [59] Giaquinto, A.; Zhang, J. J., Bialgebra actions, twists, and universal deformation formulas, J. Pure Appl. Algebra, 128, 133-151 (1998) · Zbl 0938.17015 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.