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On T-duality transformations for the three-sphere. (English) Zbl 1348.81382
Summary: We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with \(H\)-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14M27 Compactifications; symmetric and spherical varieties
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References:
[1] Shelton, J.; Taylor, W.; Wecht, B., Nongeometric flux compactifications, J. High Energy Phys., 0510, 085, (2005)
[2] Dasgupta, K.; Rajesh, G.; Sethi, S., M theory, orientifolds and G-flux, J. High Energy Phys., 9908, 023, (1999) · Zbl 1060.81575
[3] Kachru, S.; Schulz, M. B.; Tripathy, P. K.; Trivedi, S. P., New supersymmetric string compactifications, J. High Energy Phys., 0303, 061, (2003)
[4] Hellerman, S.; McGreevy, J.; Williams, B., Geometric constructions of nongeometric string theories, J. High Energy Phys., 0401, 024, (2004) · Zbl 1243.81156
[5] Dabholkar, A.; Hull, C., Duality twists, orbifolds, and fluxes, J. High Energy Phys., 0309, 054, (2003)
[6] Hull, C., A geometry for non-geometric string backgrounds, J. High Energy Phys., 0510, 065, (2005)
[7] Mathai, V.; Rosenberg, J. M., T duality for torus bundles with H fluxes via noncommutative topology, Commun. Math. Phys., 253, 705-721, (2004) · Zbl 1078.58006
[8] Mathai, V.; Rosenberg, J. M., On mysteriously missing T-duals, H-flux and the T-duality group · Zbl 1121.81107
[9] Grange, P.; Schäfer-Nameki, S., T-duality with H-flux: non-commutativity, T-folds and \(\operatorname{G} \times \operatorname{G}\) structure, Nucl. Phys. B, 770, 123-144, (2007) · Zbl 1117.81351
[10] Lüst, D., T-duality and closed string non-commutative (doubled) geometry, J. High Energy Phys., 1012, 084, (2010) · Zbl 1294.81255
[11] Lüst, D., Twisted Poisson structures and non-commutative/non-associative closed string geometry, PoS, CORFU2011, 086, (2011)
[12] Condeescu, C.; Florakis, I.; Lüst, D., Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory, J. High Energy Phys., 1204, 121, (2012) · Zbl 1348.81362
[13] Chatzistavrakidis, A.; Jonke, L., Matrix theory origins of non-geometric fluxes, J. High Energy Phys., 1302, 040, (2013) · Zbl 1342.81410
[14] Andriot, D.; Larfors, M.; Lüst, D.; Patalong, P., (non-)commutative closed string on T-dual toroidal backgrounds, J. High Energy Phys., 1306, 021, (2013) · Zbl 1342.81630
[15] Bakas, I.; Lüst, D., 3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua
[16] Blair, C. D.A., Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds · Zbl 1388.81489
[17] Blumenhagen, R., A course on noncommutative geometry in string theory · Zbl 1338.81314
[18] Bouwknegt, P.; Hannabuss, K.; Mathai, V., Nonassociative tori and applications to T-duality, Commun. Math. Phys., 264, 41-69, (2006) · Zbl 1115.46063
[19] Bouwknegt, P.; Hannabuss, K.; Mathai, V., T-duality for principal torus bundles and dimensionally reduced Gysin sequences, Adv. Theor. Math. Phys., 9, 749-773, (2005) · Zbl 1129.53013
[20] Ellwood, I.; Hashimoto, A., Effective descriptions of branes on non-geometric tori, J. High Energy Phys., 0612, 025, (2006) · Zbl 1226.81186
[21] Blumenhagen, R.; Plauschinn, E., Nonassociative gravity in string theory?, J. Phys. A, 44, 015401, (2011) · Zbl 1208.83101
[22] Blumenhagen, R.; Deser, A.; Lüst, D.; Plauschinn, E.; Rennecke, F., Non-geometric fluxes, asymmetric strings and nonassociative geometry, J. Phys. A, 44, 385401, (2011) · Zbl 1229.81220
[23] Blumenhagen, R., Nonassociativity in string theory · Zbl 1338.81314
[24] Mylonas, D.; Schupp, P.; Szabo, R. J., Membrane sigma-models and quantization of non-geometric flux backgrounds, J. High Energy Phys., 1209, 012, (2012) · Zbl 1397.81409
[25] Plauschinn, E., Non-geometric fluxes and non-associative geometry, PoS, CORFU2011, 061, (2011)
[26] Deser, A., Lie algebroids, non-associative structures and non-geometric fluxes · Zbl 1338.81319
[27] Mylonas, D.; Schupp, P.; Szabo, R. J., Non-geometric fluxes, quasi-Hopf twist deformations and nonassociative quantum mechanics · Zbl 1330.81135
[28] Mylonas, D.; Schupp, P.; Szabo, R. J., Nonassociative geometry and twist deformations in non-geometric string theory, PoS, ICMP2013, 007, (2013)
[29] Flournoy, A.; Wecht, B.; Williams, B., Constructing nongeometric vacua in string theory, Nucl. Phys. B, 706, 127-149, (2005) · Zbl 1119.81365
[30] Flournoy, A.; Williams, B., Nongeometry, duality twists, and the worldsheet, J. High Energy Phys., 0601, 166, (2006)
[31] Hellerman, S.; Walcher, J., Worldsheet CFTs for flat monodrofolds
[32] Condeescu, C.; Florakis, I.; Kounnas, C.; Lüst, D., Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s · Zbl 1342.83463
[33] Dabholkar, A.; Hull, C., Generalised T-duality and non-geometric backgrounds, J. High Energy Phys., 0605, 009, (2006)
[34] Hull, C. M., Doubled geometry and T-folds, J. High Energy Phys., 0707, 080, (2007)
[35] Andriot, D.; Larfors, M.; Lüst, D.; Patalong, P., A ten-dimensional action for non-geometric fluxes, J. High Energy Phys., 1109, 134, (2011) · Zbl 1301.81178
[36] Andriot, D.; Hohm, O.; Larfors, M.; Lüst, D.; Patalong, P., A geometric action for non-geometric fluxes, Phys. Rev. Lett., 108, 261602, (2012)
[37] Andriot, D.; Hohm, O.; Larfors, M.; Lüst, D.; Patalong, P., Non-geometric fluxes in supergravity and double field theory, Fortschr. Phys., 60, 1150-1186, (2012) · Zbl 1255.83123
[38] Blumenhagen, R.; Deser, A.; Plauschinn, E.; Rennecke, F., A bi-invariant Einstein-Hilbert action for the non-geometric string, Phys. Lett. B, 720, 215-218, (2013) · Zbl 1372.83056
[39] Blumenhagen, R.; Deser, A.; Plauschinn, E.; Rennecke, F., Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids, J. High Energy Phys., 1302, 122, (2013) · Zbl 1342.81402
[40] Blumenhagen, R.; Deser, A.; Plauschinn, E.; Rennecke, F.; Schmid, C., The intriguing structure of non-geometric frames in string theory · Zbl 1338.81315
[41] Andriot, D.; Betz, A., β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
[42] Andriot, D.; Betz, A., NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes, J. High Energy Phys., 1407, 059, (2014)
[43] Halmagyi, N., Non-geometric string backgrounds and worldsheet algebras, J. High Energy Phys., 0807, 137, (2008)
[44] Halmagyi, N., Non-geometric backgrounds and the first order string sigma model
[45] Rennecke, F., \(O(d, d)\)-duality in string theory · Zbl 1333.81357
[46] Aldazabal, G.; Marques, D.; Nunez, C., Double field theory: a pedagogical review, Class. Quantum Gravity, 30, 163001, (2013) · Zbl 1273.83001
[47] Hohm, O.; Lüst, D.; Zwiebach, B., The spacetime of double field theory: review, remarks, and outlook · Zbl 1338.81328
[48] de la Ossa, X. C.; Quevedo, F., Duality symmetries from non-abelian isometries in string theory, Nucl. Phys. B, 403, 377-394, (1993) · Zbl 1030.81513
[49] Giveon, A.; Rocek, M., On non-abelian duality, Nucl. Phys. B, 421, 173-190, (1994)
[50] Alvarez, E.; Alvarez-Gaume, L.; Barbon, J.; Lozano, Y., Some global aspects of duality in string theory, Nucl. Phys. B, 415, 71-100, (1994) · Zbl 1007.81529
[51] Sfetsos, K., Gauged WZW models and non-abelian duality, Phys. Rev. D, 50, 2784-2798, (1994)
[52] Alvarez, E.; Alvarez-Gaume, L.; Lozano, Y., On non-abelian duality, Nucl. Phys. B, 424, 155-183, (1994) · Zbl 0990.81648
[53] Klimcik, C.; Severa, P., Dual non-abelian duality and the Drinfeld double, Phys. Lett. B, 351, 455-462, (1995)
[54] Lozano, Y., Non-abelian duality and canonical transformations, Phys. Lett. B, 355, 165-170, (1995)
[55] Curtright, T.; Uematsu, T.; Zachos, C. K., Geometry and duality in supersymmetric sigma models, Nucl. Phys. B, 469, 488-512, (1996) · Zbl 0905.58065
[56] Sfetsos, K.; Thompson, D. C., On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys. B, 846, 21-42, (2011) · Zbl 1208.81173
[57] Itsios, G.; Lozano, Y.; Colgain, E. O.; Sfetsos, K., Non-abelian T-duality and consistent truncations in type-II supergravity, J. High Energy Phys., 1208, 132, (2012) · Zbl 1397.83197
[58] Itsios, G.; Nunez, C.; Sfetsos, K.; Thompson, D. C., Non-abelian T-duality and the AdS/CFT correspondence: new \(N = 1\) backgrounds, Nucl. Phys. B, 873, 1-64, (2013) · Zbl 1282.81147
[59] Sfetsos, K., Integrable interpolations: from exact CFTs to non-abelian T-duals, Nucl. Phys. B, 880, 225-246, (2014) · Zbl 1284.81257
[60] Plauschinn, E., T-duality revisited, J. High Energy Phys., 1401, 131, (2014) · Zbl 1333.81268
[61] Hull, C.; Spence, B. J., The gauged nonlinear sigma model with Wess-Zumino term, Phys. Lett. B, 232, 204, (1989)
[62] Hull, C.; Spence, B. J., The geometry of the gauged sigma model with Wess-Zumino term, Nucl. Phys. B, 353, 379-426, (1991)
[63] Hull, C., Global aspects of T-duality, gauged sigma models and T-folds, J. High Energy Phys., 0710, 057, (2007)
[64] Witten, E., Global aspects of current algebra, Nucl. Phys. B, 223, 422-432, (1983)
[65] Rocek, M.; Verlinde, E. P., Duality, quotients, and currents, Nucl. Phys. B, 373, 630-646, (1992)
[66] Hitchin, N., Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser., 54, 281-308, (2003) · Zbl 1076.32019
[67] Gualtieri, M., Generalized complex geometry · Zbl 1235.32020
[68] Grana, M.; Minasian, R.; Petrini, M.; Waldram, D., T-duality, generalized geometry and non-geometric backgrounds, J. High Energy Phys., 0904, 075, (2009)
[69] Buscher, T., A symmetry of the string background field equations, Phys. Lett. B, 194, 59, (1987)
[70] Buscher, T., Path integral derivation of quantum duality in nonlinear sigma models, Phys. Lett. B, 201, 466, (1988)
[71] Buscher, T., Quantum corrections and extended supersymmetry in new σ models, Phys. Lett. B, 159, 127, (1985)
[72] Kiritsis, E. B., Duality in gauged WZW models, Mod. Phys. Lett. A, 6, 2871-2880, (1991) · Zbl 1020.81851
[73] Kiritsis, E., Exact duality symmetries in CFT and string theory, Nucl. Phys. B, 405, 109-142, (1993) · Zbl 0917.53027
[74] Giveon, A.; Kiritsis, E., Axial vector duality as a gauge symmetry and topology change in string theory, Nucl. Phys. B, 411, 487-508, (1994) · Zbl 0973.81527
[75] Bouwknegt, P.; Evslin, J.; Mathai, V., T duality: topology change from H flux, Commun. Math. Phys., 249, 383-415, (2004) · Zbl 1062.81119
[76] Israel, D.; Kounnas, C.; Orlando, D.; Petropoulos, P. M., Electric/magnetic deformations of \(S^3\) and AdS(3), and geometric cosets, Fortschr. Phys., 53, 73-104, (2005) · Zbl 1061.83017
[77] Orlando, D.; Uruchurtu, L. I., Warped anti-de Sitter spaces from brane intersections in type II string theory, J. High Energy Phys., 1006, 049, (2010) · Zbl 1290.81133
[78] Witten, E., On string theory and black holes, Phys. Rev. D, 44, 314-324, (1991) · Zbl 0900.53037
[79] Bouwknegt, P.; Evslin, J.; Mathai, V., On the topology and H flux of T dual manifolds, Phys. Rev. Lett., 92, 181601, (2004) · Zbl 1267.81264
[80] Bouwknegt, P.; Hannabuss, K.; Mathai, V., T duality for principal torus bundles, J. High Energy Phys., 0403, 018, (2004)
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