Supermembrane origin of type II gauged supergravities in 9D. (English) Zbl 1398.81188
Summary: The M-theory origin of the IIB gauged supergravities in nine dimensions, classified according to the inequivalent classes of monodromy, is shown to exactly corresponds to the global description of the supermembrane with central charges. The global description is a realization of the sculpting mechanism of gauging [“A new mechanism for gauging a theory”, Preprint, arXiv:1107.3255] and it is associated to particular deformation of fibrations. The supermembrane with central charges may be formulated in terms of sections on symplectic torus bundles with \(\mathrm{SL}(2,\mathbb{Z})\) monodromy. This global formulation corresponds to the gauging of the abelian subgroups of \(\mathrm{SL}(2,Z)\) associated to monodromies acting on the target torus. We show the existence of the trombone symmetry in the supermembrane formulated as a nonlinear realization of the \(\mathrm{SL}(2,\mathbb Z)\) symmetry and construct its gauging in terms of the supermembrane formulated on an inequivalent class of symplectic torus fibration. The supermembrane also exhibits invariance under T-duality and we find the explicit T-duality transformation. It has a natural interpretation in terms of the cohomology of the base manifold and the homology of the target torus. We conjecture that this construction also holds for the IIA origin of gauged supergravities in 9D such that the supermembrane becomes the origin of all type II supergravities in 9D. The geometric structure of the symplectic torus bundle goes beyond the classification on conjugated classes of \(\mathrm{SL}(2,\mathbb Z)\). It depends on the elements of the coinvariant group associated to the monodromy group. The possible values of the \((p,q)\) charges on a given symplectic torus bundle are restricted to the corresponding equivalence class defining the element of the coinvariant group.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
| 83E50 | Supergravity |
References:
| [1] | Cremmer, E.; Julia, B.; Scherk, J., Supergravity theory in eleven-dimensions, Phys. Lett., B 76, 409, (1978) |
| [2] | Meessen, P.; Ortín, T., An \( {\text{SL}}\left( {{2},\mathbb{Z}} \right) \) multiplet of nine-dimensional type-II supergravity theories, Nucl. Phys., B 541, 195, (1999) · Zbl 0953.83031 |
| [3] | Gheerardyn, J.; Meessen, P., Supersymmetry of massive D = 9 supergravity, Phys. Lett., B 525, 322, (2002) · Zbl 0981.83059 |
| [4] | Bergshoeff, E.; Wit, T.; Gran, U.; Linares, R.; Roest, D., (non)abelian gauged supergravities in nine-dimensions, JHEP, 10, 061, (2002) |
| [5] | Diffon, A.; Samtleben, H., Supergravities without an action: gauging the trombone, Nucl. Phys., B 811, 1, (2009) · Zbl 1194.83100 |
| [6] | Riccioni, F., Local E_{11} and the gauging of the trombone symmetry, Class. Quant. Grav., 27, 125009, (2010) · Zbl 1213.83133 |
| [7] | Wit, B.; Nicolai, H.; Samtleben, H., Gauged supergravities, tensor hierarchies and M-theory, JHEP, 02, 044, (2008) |
| [8] | Wit, B.; Samtleben, H.; Trigiante, M., On Lagrangians and gaugings of maximal supergravities, Nucl. Phys., B 655, 93, (2003) · Zbl 1009.83063 |
| [9] | Fernandez-Melgarejo, J.; Ortín, T.; Torrente-Lujan, E., The general gaugings of maximal D = 9 supergravity, JHEP, 10, 068, (2011) · Zbl 1303.81161 |
| [10] | Martin, I.; Restuccia, A.; Torrealba, RS, On the stability of compactified D = 11 supermembranes, Nucl. Phys., B 521, 117, (1998) · Zbl 1047.81552 |
| [11] | Martin, I.; Ovalle, J.; Restuccia, A., D-branes, symplectomorphisms and noncommutative gauge theories, Nucl. Phys. Proc. Suppl., 102, 169, (2001) · Zbl 1006.81064 |
| [12] | Martin, I.; Ovalle, J.; Restuccia, A., Compactified D = 11 supermembranes and symplectic noncommutative gauge theories, Phys. Rev., D 64, 046001, (2001) |
| [13] | Hohm, O.; Kwak, SK; Zwiebach, B., Double field theory of type II strings, JHEP, 09, 013, (2011) · Zbl 1301.81219 |
| [14] | Hohm, O.; Kwak, SK, Massive type II in double field theory, JHEP, 11, 086, (2011) · Zbl 1306.81248 |
| [15] | Hull, CM; Townsend, P., Unity of superstring dualities, Nucl. Phys., B 438, 109, (1995) · Zbl 1052.83532 |
| [16] | C.M. Hull, Duality and strings, space and time, hep-th/9911080 [INSPIRE]. |
| [17] | Hull, CM, A geometry for non-geometric string backgrounds, JHEP, 10, 065, (2005) |
| [18] | Alvarez, E.; Álvarez-Gaumé, L.; Barbon, J.; Lozano, Y., Some global aspects of duality in string theory, Nucl. Phys., B 415, 71, (1994) · Zbl 1007.81529 |
| [19] | Hull, CM, Global aspects of T-duality, gauged σ-models and T-folds, JHEP, 10, 057, (2007) |
| [20] | Dabholkar, A.; Hull, CM, Duality twists, orbifolds and fluxes, JHEP, 09, 054, (2003) |
| [21] | Shelton, J.; Taylor, W.; Wecht, B., Nongeometric flux compactifications, JHEP, 10, 085, (2005) |
| [22] | Flournoy, A.; Williams, B., Nongeometry, duality twists and the worldsheet, JHEP, 01, 166, (2006) |
| [23] | Kawai, S.; Sugawara, Y., D-branes in T-fold conformal field theory, JHEP, 02, 027, (2008) |
| [24] | M. Cederwall, M-branes on U-folds, arXiv:0712.4287 [INSPIRE]. |
| [25] | Dabholkar, A.; Hull, CM, Generalised T-duality and non-geometric backgrounds, JHEP, 05, 009, (2006) |
| [26] | Hull, CM; Reid-Edwards, R., Flux compactifications of string theory on twisted tori, Fortsch. Phys., 57, 862, (2009) · Zbl 1178.81222 |
| [27] | Reid-Edwards, R., Flux compactifications, twisted tori and doubled geometry, JHEP, 06, 085, (2009) |
| [28] | Samtleben, H., Lectures on gauged supergravity and flux compactifications, Class. Quant. Grav., 25, 214002, (2008) · Zbl 1152.83306 |
| [29] | Nishino, H.; Rajpoot, S., Lorentz-covariant non-abelian gauging of a supermembrane, Phys. Rev., D 77, 106002, (2008) |
| [30] | Nishino, H.; Rajpoot, S., Gauged N = 2 supergravity in nine-dimensions and domain wall solutions, Phys. Lett., B 546, 261, (2002) · Zbl 0999.83063 |
| [31] | Cremmer, E.; Lü, H.; Pope, C.; Stelle, K., Spectrum generating symmetries for BPS solitons, Nucl. Phys., B 520, 132, (1998) · Zbl 0953.83027 |
| [32] | Aldabe, F., A supermembrane description of string-string duality, Phys. Lett., B 404, 271, (1997) |
| [33] | F. Aldabe, T duality and gauge symmetry in supermembrane theory, hep-th/9604110 [INSPIRE]. |
| [34] | Russo, J., T duality in M-theory and supermembranes, Phys. Lett., B 400, 37, (1997) |
| [35] | B. Biran, F. Englert, B. de Wit and H. Nicolai, Gauged N = 8 supergravity and its breaking from spontaneous compactification, Phys. Lett.B 124 (1983) 45 [Erratum ibid.B 128 (1983) 461] [INSPIRE]. |
| [36] | Hull, CM, The construction of new gauged N = 8 supergravities, Physica, 15D, 230, (1985) |
| [37] | Gates, SJ; Nishino, H.; Sezgin, E., Supergravity in D = 9 and its coupling to noncompact σ-model, Class. Quant. Grav., 3, 21, (1986) |
| [38] | Roest, D., M-theory and gauged supergravities, Fortsch. Phys., 53, 119, (2005) · Zbl 1072.81049 |
| [39] | Lavrinenko, IV; Lü, H.; Pope, CN, Fiber bundles and generalized dimensional reduction, Class. Quant. Grav., 15, 2239, (1998) · Zbl 0939.83052 |
| [40] | Lavrinenko, IV; Lü, H.; Pope, CN, From topology to generalized dimensional reduction, Nucl. Phys., B 492, 278, (1997) |
| [41] | Cvetič, M.; Lü, H.; Pope, CN; Stelle, K., T duality in the Green-Schwarz formalism and the massless/massive IIA duality map, Nucl. Phys., B 573, 149, (2000) · Zbl 0947.81095 |
| [42] | Abou-Zeid, M.; Wit, B.; Lüst, D.; Nicolai, H., Space-time supersymmetry, IIA/B duality and M-theory, Phys. Lett., B 466, 144, (1999) · Zbl 0987.81087 |
| [43] | Hull, CM, Massive string theories from M-theory and F-theory, JHEP, 11, 027, (1998) · Zbl 0949.81033 |
| [44] | Hull, CM, Gauged D = 9 supergravities and Scherk-Schwarz reduction, Class. Quant. Grav., 21, 509, (2004) · Zbl 1045.83063 |
| [45] | Bergshoeff, E.; Gran, U.; Roest, D., Type IIB seven-brane solutions from nine-dimensional domain walls, Class. Quant. Grav., 19, 4207, (2002) · Zbl 1003.83037 |
| [46] | Bergshoeff, E.; Sezgin, E.; Townsend, PK, Supermembranes and eleven-dimensional supergravity, Phys. Lett., B 189, 75, (1987) |
| [47] | J. Hoppe, Two problems in quantum mechanics, Ph.D. thesis, Massachusetts Institute of Technology, U.S.A. (1980). |
| [48] | Wit, B.; Hoppe, J.; Nicolai, H., On the quantum mechanics of supermembranes, Nucl. Phys., B 305, 545, (1988) |
| [49] | Wit, B.; Marquard, U.; Nicolai, H., Area preserving diffeomorphisms and supermembrane Lorentz invariance, Commun. Math. Phys., 128, 39, (1990) · Zbl 0702.58028 |
| [50] | M. Garcia del Moral, I. Martin and A. Restuccia, Nonperturbative\( {\text{SL}}\left( {{2},\mathbb{Z}} \right) \) (\(p\),\(q\))-strings manifestly realized on the quantum M2, arXiv:0802.0573 [INSPIRE]. |
| [51] | Garcia del Moral, M.; Restuccia, A., On the spectrum of a noncommutative formulation of the D = 11 supermembrane with winding, Phys. Rev., D 66, 045023, (2002) |
| [52] | Boulton, L.; Garcia del Moral, M.; Martin, I.; Restuccia, A., On the spectrum of a matrix model for the D = 11 supermembrane compactified on a torus with nontrivial winding, Class. Quant. Grav., 19, 2951, (2002) · Zbl 1002.83052 |
| [53] | Boulton, L.; Garcia del Moral, M.; Restuccia, A., Discreteness of the spectrum of the compactified D = 11 supermembrane with nontrivial winding, Nucl. Phys., B 671, 343, (2003) · Zbl 1058.81637 |
| [54] | Boulton, L.; Restuccia, A., The heat kernel of the compactified D = 11 supermembrane with non-trivial winding, Nucl. Phys., B 724, 380, (2005) · Zbl 1178.81215 |
| [55] | Bellorín, J.; Restuccia, A., D = 11 supermembrane wrapped on calibrated submanifolds, Nucl. Phys., B 737, 190, (2006) · Zbl 1109.81064 |
| [56] | Boulton, L.; Garcia del Moral, M.; Restuccia, A., The supermembrane with central charges: (2 + 1)-D NCSYM, confinement and phase transition, Nucl. Phys., B 795, 27, (2008) · Zbl 1219.81207 |
| [57] | Boulton, L.; Moral, MPG; Restuccia, A., Spectral properties in supersymmetric matrix models, Nucl. Phys., B 856, 716, (2012) · Zbl 1246.81222 |
| [58] | Connes, A.; Douglas, MR; Schwarz, AS, Noncommutative geometry and matrix theory: compactification on tori, JHEP, 02, 003, (1998) · Zbl 1018.81052 |
| [59] | Wit, B.; Peeters, K.; Plefka, J., Superspace geometry for supermembrane backgrounds, Nucl. Phys., B 532, 99, (1998) · Zbl 1041.83526 |
| [60] | Lüst, D., T-duality and closed string non-commutative (doubled) geometry, JHEP, 12, 084, (2010) · Zbl 1294.81255 |
| [61] | M.P.G. del Moral, A New Mechanism for Gauging a Theory, arXiv:1107.3255 [INSPIRE]. |
| [62] | Martin, I.; Restuccia, A., Magnetic monopoles over topologically nontrivial Riemann surfaces, Lett. Math. Phys., 39, 379, (1997) · Zbl 0923.53010 |
| [63] | Martin, I.; Restuccia, A., Symplectic connections, noncommutative Yang-Mills theory and supermembranes, Nucl. Phys., B 622, 240, (2002) · Zbl 0988.81103 |
| [64] | Garcia del Moral, MP; etal., \( {\text{SL}}\left( {{2},\mathbb{Z}} \right) \) symmetries, supermembranes and symplectic torus bundles, JHEP, 09, 068, (2011) · Zbl 1301.81202 |
| [65] | D. Baraglia, Topological T-duality for torus bundles with monodromy, arXiv:1201.1731. · Zbl 1325.53035 |
| [66] | Khan, PJ, Symplectic torus bundles and group extensions, New York J. Math., 11, 3555, (2005) · Zbl 1090.57021 |
| [67] | Wit, B.; Peeters, K.; Plefka, J., Supermembranes with winding, Phys. Lett., B 409, 117, (1997) |
| [68] | Wit, B.; Lüscher, M.; Nicolai, H., The supermembrane is unstable, Nucl. Phys., B 320, 135, (1989) |
| [69] | P. Cowdall, Novel domain wall and Minkowski vacua of D = 9 maximal SO(2) gauged supergravity, hep-th/0009016 [INSPIRE]. · Zbl 0986.83048 |
| [70] | Howe, PS; Lambert, N.; West, PC, A new massive type IIA supergravity from compactification, Phys. Lett., B 416, 303, (1998) |
| [71] | Honda, K., On the classification of tight contact structures II, Geom. Topol., 4, 309, (2000) · Zbl 0980.57010 |
| [72] | M. Berasaluce-Gonzalez, P. Camara, F. Marchesano, D. Regalado and A. Uranga, Non-Abelian discrete gauge symmetries in 4D string models, arXiv:1206.2383 [INSPIRE]. |
| [73] | L. Ibáñez, A. Schellekens and A. Uranga, Discrete gauge symmetries in discrete MSSM-like orientifolds, arXiv:1205.5364 [INSPIRE]. · Zbl 1262.81239 |
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