Local \(\beta\)-deformations and Yang-Baxter sigma model. (English) Zbl 1395.81192
Summary: Homogeneous Yang-Baxter (YB) deformation of \(\mathrm{AdS}_{5} \times S^5\) superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to \(\beta\)-deformations of the \(\mathrm{AdS}_{5} \times S^5\) background when the classical \(r\)-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10,10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing \(H\)-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study \(\beta\)-deformations of \(H\)-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E50 | Supergravity |
| 16T25 | Yang-Baxter equations |
References:
| [1] | Klimčík, C., Yang-Baxter σ-models and ds/AdS T duality, JHEP, 12, 051, (2002) · doi:10.1088/1126-6708/2002/12/051 |
| [2] | Klimčík, C., On integrability of the Yang-Baxter σ-model, J. Math. Phys., 50, (2009) · Zbl 1215.81099 · doi:10.1063/1.3116242 |
| [3] | Delduc, F.; Magro, M.; Vicedo, B., On classical q-deformations of integrable σ-models, JHEP, 11, 192, (2013) · Zbl 1342.81182 · doi:10.1007/JHEP11(2013)192 |
| [4] | Matsumoto, T.; Yoshida, K., Yang-Baxter σ-models based on the CYBE, Nucl. Phys., B 893, 287, (2015) · Zbl 1348.81379 · doi:10.1016/j.nuclphysb.2015.02.009 |
| [5] | Delduc, F.; Magro, M.; Vicedo, B., an integrable deformation of the AdS_{5} × \(S\)\^{}{5}superstring action, Phys. Rev. Lett., 112, (2014) · Zbl 1333.81322 · doi:10.1103/PhysRevLett.112.051601 |
| [6] | Delduc, F.; Magro, M.; Vicedo, B., derivation of the action and symmetries of the q-deformed AdS_{5} × \(S\)\^{}{5}superstring, JHEP, 10, 132, (2014) · Zbl 1333.81322 · doi:10.1007/JHEP10(2014)132 |
| [7] | Kawaguchi, I.; Matsumoto, T.; Yoshida, K., Jordanian deformations of the AdS_{5} × \(S\)\^{}{5}superstring, JHEP, 04, 153, (2014) · doi:10.1007/JHEP04(2014)153 |
| [8] | Matsumoto, T.; Yoshida, K., Lunin-Maldacena backgrounds from the classical Yang-Baxter equation - towards the gravity/CYBE correspondence, JHEP, 06, 135, (2014) · Zbl 1333.83196 · doi:10.1007/JHEP06(2014)135 |
| [9] | Matsumoto, T.; Yoshida, K., Integrability of classical strings dual for noncommutative gauge theories, JHEP, 06, 163, (2014) · Zbl 1333.81262 · doi:10.1007/JHEP06(2014)163 |
| [10] | Matsumoto, T.; Yoshida, K., Schrödinger geometries arising from Yang-Baxter deformations, JHEP, 04, 180, (2015) · Zbl 1388.83866 · doi:10.1007/JHEP04(2015)180 |
| [11] | Tongeren, SJ, on classical Yang-Baxter based deformations of the AdS_{5} × \(S\)\^{}{5}superstring, JHEP, 06, 048, (2015) · Zbl 1388.83332 · doi:10.1007/JHEP06(2015)048 |
| [12] | Tongeren, SJ, Yang-Baxter deformations, AdS/CFT and twist-noncommutative gauge theory, Nucl. Phys., B 904, 148, (2016) · Zbl 1332.81197 · doi:10.1016/j.nuclphysb.2016.01.012 |
| [13] | H. Kyono and K. Yoshida, Supercoset construction of Yang-Baxter deformed AdS_{5} × \(S\)\^{}{5}backgrounds, PTEP2016 (2016) 083B03 [arXiv:1605.02519] [INSPIRE]. |
| [14] | Lunin, O.; Maldacena, JM, deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP, 05, 033, (2005) · doi:10.1088/1126-6708/2005/05/033 |
| [15] | Frolov, S., Lax pair for strings in lunin-Maldacena background, JHEP, 05, 069, (2005) · doi:10.1088/1126-6708/2005/05/069 |
| [16] | Hashimoto, A.; Itzhaki, N., Noncommutative Yang-Mills and the AdS/CFT correspondence, Phys. Lett., B 465, 142, (1999) · Zbl 0987.81108 · doi:10.1016/S0370-2693(99)01037-0 |
| [17] | Maldacena, JM; Russo, JG, Large N limit of noncommutative gauge theories, JHEP, 09, 025, (1999) · Zbl 0957.81083 · doi:10.1088/1126-6708/1999/09/025 |
| [18] | Herzog, CP; Rangamani, M.; Ross, SF, Heating up Galilean holography, JHEP, 11, 080, (2008) · doi:10.1088/1126-6708/2008/11/080 |
| [19] | Maldacena, J.; Martelli, D.; Tachikawa, Y., Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP, 10, 072, (2008) · Zbl 1245.81200 · doi:10.1088/1126-6708/2008/10/072 |
| [20] | Adams, A.; Balasubramanian, K.; McGreevy, J., Hot spacetimes for cold atoms, JHEP, 11, 059, (2008) · doi:10.1088/1126-6708/2008/11/059 |
| [21] | Osten, D.; Tongeren, SJ, Abelian Yang-Baxter deformations and tst transformations, Nucl. Phys., B 915, 184, (2017) · Zbl 1354.81048 · doi:10.1016/j.nuclphysb.2016.12.007 |
| [22] | Borsato, R.; Wulff, L., Target space supergeometry of η and λ-deformed strings, JHEP, 10, 045, (2016) · Zbl 1390.81412 · doi:10.1007/JHEP10(2016)045 |
| [23] | Orlando, D.; Reffert, S.; Sakamoto, J.; Yoshida, K., Generalized type IIB supergravity equations and non-abelian classical r-matrices, J. Phys., A 49, 445403, (2016) · Zbl 1354.83054 |
| [24] | Hoare, B.; Tseytlin, AA, homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_{5}σ-model, J. Phys., A 49, 494001, (2016) · Zbl 1357.81149 |
| [25] | Borsato, R.; Wulff, L., Integrable deformations of T -dual σ models, Phys. Rev. Lett., 117, 251602, (2016) · Zbl 1332.81170 · doi:10.1103/PhysRevLett.117.251602 |
| [26] | Hoare, B.; Thompson, DC, Marginal and non-commutative deformations via non-abelian T-duality, JHEP, 02, 059, (2017) · Zbl 1377.83056 · doi:10.1007/JHEP02(2017)059 |
| [27] | Borsato, R.; Wulff, L., On non-abelian T-duality and deformations of supercoset string σ-models, JHEP, 10, 024, (2017) · Zbl 1383.83155 · doi:10.1007/JHEP10(2017)024 |
| [28] | Lüst, D.; Osten, D., Generalised fluxes, Yang-Baxter deformations and the O(d, d) structure of non-abelian T-duality, JHEP, 05, 165, (2018) · Zbl 1391.83115 · doi:10.1007/JHEP05(2018)165 |
| [29] | Fridling, BE; Jevicki, A., Dual representations and ultraviolet divergences in nonlinear σ models, Phys. Lett., B 134, 70, (1984) · doi:10.1016/0370-2693(84)90987-0 |
| [30] | Fradkin, ES; Tseytlin, AA, Quantum equivalence of dual field theories, Annals Phys., 162, 31, (1985) · doi:10.1016/0003-4916(85)90225-8 |
| [31] | Ossa, XC; Quevedo, F., Duality symmetries from nonabelian isometries in string theory, Nucl. Phys., B 403, 377, (1993) · Zbl 1030.81513 · doi:10.1016/0550-3213(93)90041-M |
| [32] | Gasperini, M.; Ricci, R.; Veneziano, G., A problem with nonabelian duality?, Phys. Lett., B 319, 438, (1993) · doi:10.1016/0370-2693(93)91748-C |
| [33] | Giveon, A.; Roček, M., On nonabelian duality, Nucl. Phys., B 421, 173, (1994) · Zbl 0990.81690 · doi:10.1016/0550-3213(94)90230-5 |
| [34] | Alvarez, E.; Álvarez-Gaumé, L.; Lozano, Y., On nonabelian duality, Nucl. Phys., B 424, 155, (1994) · Zbl 0990.81648 · doi:10.1016/0550-3213(94)90093-0 |
| [35] | Elitzur, S.; Giveon, A.; Rabinovici, E.; Schwimmer, A.; Veneziano, G., Remarks on nonabelian duality, Nucl. Phys., B 435, 147, (1995) · Zbl 1020.81834 · doi:10.1016/0550-3213(94)00426-F |
| [36] | Sfetsos, K.; Thompson, DC, On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys., B 846, 21, (2011) · Zbl 1208.81173 · doi:10.1016/j.nuclphysb.2010.12.013 |
| [37] | Y. Lozano, E. Ó Colgáin, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond Fields and Coset Geometries, JHEP06 (2011) 106 [arXiv:1104.5196] [INSPIRE]. · Zbl 0967.81519 |
| [38] | Itsios, G.; Núñez, C.; Sfetsos, K.; Thompson, DC, non-abelian T-duality and the AdS/CFT correspondence:new N = 1 backgrounds, Nucl. Phys., B 873, 1, (2013) · Zbl 1282.81147 · doi:10.1016/j.nuclphysb.2013.04.004 |
| [39] | Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, AA, scale invariance of the η-deformed AdS_{5} × \(S\)\^{}{5}superstring, T-duality and modified type-II equations, Nucl. Phys., B 903, 262, (2016) · Zbl 1332.81167 · doi:10.1016/j.nuclphysb.2015.12.012 |
| [40] | A.A. Tseytlin and L. Wulff, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP06 (2016) 174 [arXiv:1605.04884] [INSPIRE]. · Zbl 1390.83426 |
| [41] | Wulff, L., Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly, Phys. Lett., B 781, 417, (2018) · Zbl 1398.83128 · doi:10.1016/j.physletb.2018.04.025 |
| [42] | M. Hong, Y. Kim and E. Ó Colgáin, On non-Abelian T-duality for non-semisimple groups, arXiv:1801.09567 [INSPIRE]. |
| [43] | Sakatani, Y.; Uehara, S.; Yoshida, K., Generalized gravity from modified DFT, JHEP, 04, 123, (2017) · Zbl 1378.83094 · doi:10.1007/JHEP04(2017)123 |
| [44] | Baguet, A.; Magro, M.; Samtleben, H., Generalized IIB supergravity from exceptional field theory, JHEP, 03, 100, (2017) · Zbl 1377.83132 · doi:10.1007/JHEP03(2017)100 |
| [45] | J. Sakamoto, Y. Sakatani and K. Yoshida, Weyl invariance for generalized supergravity backgrounds from the doubled formalism, PTEP2017 (2017) 053B07 [arXiv:1703.09213] [INSPIRE]. · Zbl 1477.83090 |
| [46] | Sakamoto, J.; Sakatani, Y.; Yoshida, K., Homogeneous Yang-Baxter deformations as generalized diffeomorphisms, J. Phys., A 50, 415401, (2017) · Zbl 1376.81063 |
| [47] | Fernandez-Melgarejo, JJ; Sakamoto, J.; Sakatani, Y.; Yoshida, K., T -folds from Yang-Baxter deformations, JHEP, 12, 108, (2017) · Zbl 1383.83206 · doi:10.1007/JHEP12(2017)108 |
| [48] | Siegel, W., Two vierbein formalism for string inspired axionic gravity, Phys. Rev., D 47, 5453, (1993) |
| [49] | Siegel, W., Superspace duality in low-energy superstrings, Phys. Rev., D 48, 2826, (1993) |
| [50] | W. Siegel, Manifest duality in low-energy superstrings, in International Conference on Strings 93 Berkeley, California, May 24-29, 1993, pp. 353-363 [hep-th/9308133] [INSPIRE]. · Zbl 0844.58101 |
| [51] | Hull, C.; Zwiebach, B., Double field theory, JHEP, 09, 099, (2009) · doi:10.1088/1126-6708/2009/09/099 |
| [52] | Hull, C.; Zwiebach, B., The gauge algebra of double field theory and Courant brackets, JHEP, 09, 090, (2009) · doi:10.1088/1126-6708/2009/09/090 |
| [53] | Hohm, O.; Hull, C.; Zwiebach, B., Generalized metric formulation of double field theory, JHEP, 08, 008, (2010) · Zbl 1291.81255 · doi:10.1007/JHEP08(2010)008 |
| [54] | Green, MB; Schwarz, JH, Covariant description of superstrings, Phys. Lett., B 136, 367, (1984) · doi:10.1016/0370-2693(84)92021-5 |
| [55] | Jeon, I.; Lee, K.; Park, J-H, Stringy differential geometry, beyond Riemann, Phys. Rev., D 84, (2011) |
| [56] | Jeon, I.; Lee, K.; Park, J-H, Incorporation of fermions into double field theory, JHEP, 11, 025, (2011) · Zbl 1306.81160 · doi:10.1007/JHEP11(2011)025 |
| [57] | I. Jeon, K. Lee and J.-H. Park, Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity, Phys. Rev.D 85 (2012) 081501 [Erratum ibid.D 86 (2012) 089903] [arXiv:1112.0069] [INSPIRE]. |
| [58] | Jeon, I.; Lee, K.; Park, J-H, Ramond-Ramond cohomology and O(D, D) T-duality, JHEP, 09, 079, (2012) · Zbl 1397.81261 · doi:10.1007/JHEP09(2012)079 |
| [59] | Jeon, I.; Lee, K.; Park, J-H; Suh, Y., stringy unification of type IIA and IIB supergravities under N = 2 \(D\) = 10 supersymmetric double field theory, Phys. Lett., B 723, 245, (2013) · Zbl 1311.83062 · doi:10.1016/j.physletb.2013.05.016 |
| [60] | Hull, CM, Doubled geometry and T-folds, JHEP, 07, 080, (2007) · doi:10.1088/1126-6708/2007/07/080 |
| [61] | Blair, CDA; Malek, E.; Routh, AJ, an O(D, D) invariant Hamiltonian action for the superstring, Class. Quant. Grav., 31, 205011, (2014) · Zbl 1304.81132 · doi:10.1088/0264-9381/31/20/205011 |
| [62] | Driezen, S.; Sevrin, A.; Thompson, DC, Aspects of the doubled worldsheet, JHEP, 12, 082, (2016) · Zbl 1390.81587 · doi:10.1007/JHEP12(2016)082 |
| [63] | Bandos, I., Superstring in doubled superspace, Phys. Lett., B 751, 408, (2015) · Zbl 1339.81070 · doi:10.1016/j.physletb.2015.10.081 |
| [64] | Park, J-H, Green-Schwarz superstring on doubled-yet-gauged spacetime, JHEP, 11, 005, (2016) · Zbl 1390.83352 · doi:10.1007/JHEP11(2016)005 |
| [65] | Bandos, I., Type II superstring in doubled superspace, Fortsch. Phys., 64, 361, (2016) · Zbl 1339.81070 · doi:10.1002/prop.201500055 |
| [66] | Hatsuda, M.; Kamimura, K.; Siegel, W., Ramond-Ramond gauge fields in superspace with manifest T-duality, JHEP, 02, 134, (2015) · Zbl 1388.83819 · doi:10.1007/JHEP02(2015)134 |
| [67] | Hatsuda, M.; Kamimura, K.; Siegel, W., Type II chiral affine Lie algebras and string actions in doubled space, JHEP, 09, 113, (2015) · Zbl 1388.81183 · doi:10.1007/JHEP09(2015)113 |
| [68] | Kawaguchi, I.; Orlando, D.; Yoshida, K., Yangian symmetry in deformed WZNW models on squashed spheres, Phys. Lett., B 701, 475, (2011) · doi:10.1016/j.physletb.2011.06.007 |
| [69] | Kawaguchi, I.; Yoshida, K., A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models, J. Math. Phys., 55, (2014) · Zbl 1316.81077 · doi:10.1063/1.4880341 |
| [70] | Delduc, F.; Magro, M.; Vicedo, B., Integrable double deformation of the principal chiral model, Nucl. Phys., B 891, 312, (2015) · Zbl 1328.81200 · doi:10.1016/j.nuclphysb.2014.12.018 |
| [71] | Delduc, F.; Hoare, B.; Kameyama, T.; Magro, M., Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and tst transformations in one integrable σ-model, JHEP, 10, 212, (2017) · Zbl 1383.81106 · doi:10.1007/JHEP10(2017)212 |
| [72] | Demulder, S.; Driezen, S.; Sevrin, A.; Thompson, DC, Classical and quantum aspects of Yang-Baxter Wess-Zumino models, JHEP, 03, 041, (2018) · Zbl 1388.83652 · doi:10.1007/JHEP03(2018)041 |
| [73] | Hohm, O.; Kwak, SK, Frame-like geometry of double field theory, J. Phys., A 44, (2011) · Zbl 1209.81168 |
| [74] | Arutyunov, G.; Borsato, R.; Frolov, S., puzzles of η-deformed AdS_{5} × \(S\)\^{}{5}, JHEP, 12, 049, (2015) · Zbl 1388.83726 |
| [75] | Jeon, I.; Lee, K.; Park, J-H, Differential geometry with a projection: application to double field theory, JHEP, 04, 014, (2011) · Zbl 1250.81085 · doi:10.1007/JHEP04(2011)014 |
| [76] | Hohm, O.; Zwiebach, B., On the Riemann tensor in double field theory, JHEP, 05, 126, (2012) · Zbl 1348.83080 · doi:10.1007/JHEP05(2012)126 |
| [77] | Fukuma, M.; Oota, T.; Tanaka, H., Comments on T dualities of Ramond-Ramond potentials on tori, Prog. Theor. Phys., 103, 425, (2000) · doi:10.1143/PTP.103.425 |
| [78] | Bergshoeff, E.; Kallosh, R.; Ortín, T.; Roest, D.; Proeyen, A., new formulations of D = 10 supersymmetry and D8-O8 domain walls, Class. Quant. Grav., 18, 3359, (2001) · Zbl 1004.83053 · doi:10.1088/0264-9381/18/17/303 |
| [79] | Hohm, O.; Lüst, D.; Zwiebach, B., The spacetime of double field theory: review, remarks and outlook, Fortsch. Phys., 61, 926, (2013) · Zbl 1338.81328 · doi:10.1002/prop.201300024 |
| [80] | Hassan, SF, SO(d, d) transformations of Ramond-Ramond fields and space-time spinors, Nucl. Phys., B 583, 431, (2000) · Zbl 0984.81117 · doi:10.1016/S0550-3213(00)00337-0 |
| [81] | Hohm, O.; Kwak, SK; Zwiebach, B., Double field theory of type II strings, JHEP, 09, 013, (2011) · Zbl 1301.81219 · doi:10.1007/JHEP09(2011)013 |
| [82] | Duff, MJ, Duality rotations in string theory, Nucl. Phys., B 335, 610, (1990) · Zbl 0967.81519 · doi:10.1016/0550-3213(90)90520-N |
| [83] | Tseytlin, AA, Duality symmetric formulation of string world sheet dynamics, Phys. Lett., B 242, 163, (1990) · doi:10.1016/0370-2693(90)91454-J |
| [84] | Tseytlin, AA, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys., B 350, 395, (1991) · doi:10.1016/0550-3213(91)90266-Z |
| [85] | Hull, CM, A geometry for non-geometric string backgrounds, JHEP, 10, 065, (2005) · doi:10.1088/1126-6708/2005/10/065 |
| [86] | Copland, NB, A double σ-model for double field theory, JHEP, 04, 044, (2012) · Zbl 1348.81363 · doi:10.1007/JHEP04(2012)044 |
| [87] | Lee, K.; Park, J-H, Covariant action for a string in “doubled yet gauged” spacetime, Nucl. Phys., B 880, 134, (2014) · Zbl 1284.81238 · doi:10.1016/j.nuclphysb.2014.01.003 |
| [88] | Cvetič, M.; Lü, H.; Pope, CN; Stelle, KS, T duality in the Green-Schwarz formalism and the massless/massive IIA duality map, Nucl. Phys., B 573, 149, (2000) · Zbl 0947.81095 |
| [89] | Metsaev, RR; Tseytlin, AA, type IIB superstring action in AdS_{5} × \(S\)\^{}{5}background, Nucl. Phys., B 533, 109, (1998) · Zbl 0956.81063 · doi:10.1016/S0550-3213(98)00570-7 |
| [90] | Förste, S., A truly marginal deformation of SL(2, R) in a null direction, Phys. Lett., B 338, 36, (1994) · doi:10.1016/0370-2693(94)91340-4 |
| [91] | Israel, D.; Kounnas, C.; Petropoulos, MP, superstrings on NS5 backgrounds, deformed AdS_{3}and holography, JHEP, 10, 028, (2003) · doi:10.1088/1126-6708/2003/10/028 |
| [92] | A. Giveon, N. Itzhaki and D. Kutasov, \( \text{T}\overline{\text{T}} \)and LST, JHEP07 (2017) 122 [arXiv:1701.05576] [INSPIRE]. |
| [93] | Giveon, A.; Itzhaki, N.; Kutasov, D., A solvable irrelevant deformation of AdS_{3}/CFT_{2}, JHEP, 12, 155, (2017) · Zbl 1383.81217 · doi:10.1007/JHEP12(2017)155 |
| [94] | M. Asrat, A. Giveon, N. Itzhaki and D. Kutasov, Holography Beyond AdS, arXiv:1711.02690 [INSPIRE]. · Zbl 1391.81138 |
| [95] | Giribet, G., \( T\overline{T} \) -deformations, AdS/CFT and correlation functions, JHEP, 02, 114, (2018) · Zbl 1387.81316 · doi:10.1007/JHEP02(2018)114 |
| [96] | Azeyanagi, T.; Hofman, DM; Song, W.; Strominger, A., the spectrum of strings on warped AdS_{3} × \(S\)\^{}{3}, JHEP, 04, 078, (2013) · Zbl 1342.83318 · doi:10.1007/JHEP04(2013)078 |
| [97] | Giveon, A.; Kiritsis, E., Axial vector duality as a gauge symmetry and topology change in string theory, Nucl. Phys., B 411, 487, (1994) · Zbl 1049.81628 · doi:10.1016/0550-3213(94)90460-X |
| [98] | Araujo, T.; Bakhmatov, I.; Colgáin, EÓ; Sakamoto, J.; Sheikh-Jabbari, MM; Yoshida, K., Yang-Baxter σ-models, conformal twists and noncommutative Yang-Mills theory, Phys. Rev., D 95, 105006, (2017) |
| [99] | Araujo, T.; Bakhmatov, I.; Colgáin, EÓ; Sakamoto, J.; Sheikh-Jabbari, MM; Yoshida, K., Conformal twists, Yang-Baxter σ-models & holographic noncommutativity, J. Phys., A 51, 235401, (2018) · Zbl 1436.81084 |
| [100] | T. Araujo, E. Ó Colgáin, J. Sakamoto, M.M. Sheikh-Jabbari and K. Yoshida, I in generalized supergravity, Eur. Phys. J.C 77 (2017) 739 [arXiv:1708.03163] [INSPIRE]. · Zbl 1215.81099 |
| [101] | Hohm, O.; Zwiebach, B., Large gauge transformations in double field theory, JHEP, 02, 075, (2013) · Zbl 1342.81292 · doi:10.1007/JHEP02(2013)075 |
| [102] | Hull, CM; Spence, BJ, The gauged nonlinear σ model with Wess-Zumino term, Phys. Lett., B 232, 204, (1989) · doi:10.1016/0370-2693(89)91688-2 |
| [103] | Hull, CM; Spence, BJ, The geometry of the gauged σ-model with Wess-Zumino term, Nucl. Phys., B 353, 379, (1991) · doi:10.1016/0550-3213(91)90342-U |
| [104] | I. Bakhmatov, E. Ó. Colgáin, M.M. Sheikh-Jabbari and H. Yavartanoo, Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT), arXiv:1803.07498 [INSPIRE]. · Zbl 1395.83118 |
| [105] | Klimčík, C.; Ševera, P., Poisson-Lie T duality and loop groups of Drinfeld doubles, Phys. Lett., B 372, 65, (1996) · Zbl 1037.81576 · doi:10.1016/0370-2693(96)00025-1 |
| [106] | C. Klimčík and P. Ševera, Dual nonAbelian duality and the Drinfeld double, Phys. Lett.B 351 (1995) 455 [hep-th/9502122] [INSPIRE]. · Zbl 1390.81412 |
| [107] | R.A. Reid-Edwards, Bi-Algebras, Generalised Geometry and T-duality, arXiv:1001.2479 [INSPIRE]. · Zbl 1388.83866 |
| [108] | F. Hassler, Poisson-Lie T-duality in Double Field Theory, arXiv:1707.08624 [INSPIRE]. · Zbl 1332.81170 |
| [109] | Rennecke, F., \(O\)(d, d)-duality in string theory, JHEP, 10, 69, (2014) · Zbl 1333.81357 · doi:10.1007/JHEP10(2014)069 |
| [110] | G. Arutyunov and S. Frolov, Foundations of the AdS_{5} × \(S\)\^{}{5}Superstring. Part I, J. Phys.A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE]. · Zbl 1388.83652 |
| [111] | L. Castellani, R. D’Auria and P. Fre, Supergravity and superstrings: A Geometric perspective. Vol. 1: Mathematical foundations, World Scientific, Singapore, Singapore (1991), pp. 1-603 [INSPIRE]. · Zbl 0753.53045 |
| [112] | T. Ortin, Gravity and strings, Cambridge University Press (2004) [INSPIRE] · Zbl 1057.83003 |
| [113] | Grisaru, MT; Howe, PS; Mezincescu, L.; Nilsson, B.; Townsend, PK, \(N\) = 2 superstrings in a supergravity background, Phys. Lett., B 162, 116, (1985) · doi:10.1016/0370-2693(85)91071-8 |
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.
