Positive mass theorem in extended supergravities. (English) Zbl 1325.83005
Summary: Following the Witten-Nester formalism, we present a useful prescription using Weyl spinors towards the positivity of mass. As a generalization of [the authors, Phys. Rev. D89, No. 2, Article No. 023011, 8 p. (2014: arxiv:1310.1663)], we show that some ”positivity conditions” must be imposed upon the gauge connections appearing in the supercovariant derivative acting on spinors. A complete classification of the connection fulfilling the positivity conditions is given. It turns out that these positivity conditions are indeed satisfied for a number of extended supergravity theories. It is shown that the positivity property holds for the Einstein-complex scalar system, provided that the target space is Hodge-Kähler and the potential is expressed in terms of the superpotential. In the Einstein-Maxwell-dilaton theory with a dilaton potential, the dilaton coupling function and the superpotential are fixed by the positive mass property. We also explore the \(N = 8\) gauged supergravity and demonstrate that the positivity of the mass holds independently of the gaugings and the deformation parameters.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C22 | Einstein-Maxwell equations |
| 83E50 | Supergravity |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 83F05 | Relativistic cosmology |
Keywords:
Witten-Nester formalismReferences:
| [1] | Schoen, R.; Yau, S. T., Commun. Math. Phys., 65, 45 (1979) · Zbl 0405.53045 |
| [2] | Schoen, R.; Yau, S.-T., Commun. Math. Phys., 79, 231 (1981) · Zbl 0494.53028 |
| [3] | Bondi, H., Rev. Mod. Phys., 29, 423 (1957) · Zbl 0079.42001 |
| [4] | Jang, P. S.; Wald, R. M., J. Math. Phys., 18, 41 (1977) |
| [5] | Huisken, G.; Ilmanen, T., J. Differ. Geom., 59, 353 (2001) · Zbl 1055.53052 |
| [6] | Witten, E., Commun. Math. Phys., 80, 381 (1981) · Zbl 1051.83532 |
| [7] | Nester, J. A., Phys. Lett. A, 83, 241 (1981) |
| [8] | Compere, G.; Copsey, K.; de Buyl, S.; Mann, R. B., J. High Energy Phys., 0912, 047 (2009) |
| [9] | Gibbons, G. W.; Warner, N. P., Class. Quantum Gravity, 31, 025016 (2014) · Zbl 1292.83031 |
| [10] | Gibbons, G. W.; Kastor, D.; London, L. A.J.; Townsend, P. K.; Traschen, J. H., Nucl. Phys. B, 416, 850 (1994) · Zbl 1007.81565 |
| [11] | Deser, S.; Teitelboim, C., Phys. Rev. Lett., 39, 249 (1977) |
| [12] | Horowitz, G. T.; Strominger, A., Phys. Rev. D, 27, 2793 (1983) |
| [13] | Hull, C. M., Commun. Math. Phys., 90, 545 (1983) |
| [14] | Deser, S., Phys. Rev. D, 27, 2805 (1983) |
| [15] | Maeda, K.-i.; Nozawa, M., Prog. Theor. Phys. Suppl., 189, 310 (2011) · Zbl 1291.83153 |
| [16] | Gibbons, G. W.; Hull, C. M., Phys. Lett. B, 109, 190 (1982) |
| [17] | Gibbons, G. W.; Hawking, S. W.; Horowitz, G. T.; Perry, M. J., Commun. Math. Phys., 88, 295 (1983) |
| [18] | Gibbons, G. W.; Hull, C. M.; Warner, N. P., Nucl. Phys. B, 218, 173 (1983) |
| [19] | Boucher, W., Nucl. Phys. B, 242, 282 (1984) |
| [20] | Townsend, P. K., Phys. Lett. B, 148, 55 (1984) |
| [21] | Gibbons, G. W.; Horowitz, G. T.; Townsend, P. K., Class. Quantum Gravity, 12, 297 (1995) · Zbl 0817.53054 |
| [22] | Kostelecky, V. A.; Perry, M. J., Phys. Lett. B, 371, 191 (1996) |
| [23] | Shiromizu, T., Phys. Rev. D, 60, 104046 (1999) |
| [24] | Rogatko, M., Class. Quantum Gravity, 19, 5063 (2002) · Zbl 1021.83013 |
| [25] | Nozawa, M., Class. Quantum Gravity, 28, 175013 (2011) · Zbl 1225.83069 |
| [26] | Nozawa, M.; Shiromizu, T., Phys. Rev. D, 89, 023011 (2014) |
| [27] | Elder, B.; Joyce, A.; Khoury, J.; Tolley, A. J. |
| [28] | Arnowitt, R. L.; Deser, S.; Misner, C. W., Gen. Relativ. Gravit., 40, 1997 (2008) · Zbl 1152.83320 |
| [29] | Cacciatori, S. L.; Klemm, D.; Mansi, D. S.; Zorzan, E., J. High Energy Phys., 0805, 097 (2008) |
| [30] | Meessen, P.; Palomo-Lozano, A., J. High Energy Phys., 0905, 042 (2009) |
| [31] | Abbott, L. F.; Deser, S., Nucl. Phys. B, 195, 76 (1982) · Zbl 0900.53033 |
| [32] | Henneaux, M.; Teitelboim, C., Commun. Math. Phys., 98, 391 (1985) · Zbl 1032.83502 |
| [33] | Ashtekar, A.; Das, S., Class. Quantum Gravity, 17, L17 (2000) · Zbl 0943.83023 |
| [34] | Hollands, S.; Ishibashi, A.; Marolf, D., Class. Quantum Gravity, 22, 2881 (2005) · Zbl 1082.83014 |
| [35] | Romans, L. J., Nucl. Phys. B, 383, 395 (1992) |
| [36] | Caldarelli, M. M.; Klemm, D., Nucl. Phys. B, 545, 434 (1999) · Zbl 0953.83020 |
| [37] | Hristov, K.; Toldo, C.; Vandoren, S., J. High Energy Phys., 1112, 014 (2011) |
| [38] | Hristov, K., J. High Energy Phys., 1203, 095 (2012) |
| [39] | Klemm, D.; Nozawa, M., J. High Energy Phys., 1305, 123 (2013) |
| [40] | Dibitetto, G.; Klemm, D., J. High Energy Phys., 1012, 005 (2010) |
| [41] | Breitenlohner, P.; Freedman, D. Z., Ann. Phys., 144, 249 (1982) · Zbl 0606.53044 |
| [42] | Hertog, T.; Horowitz, G. T.; Maeda, K., Phys. Rev. D, 69, 105001 (2004) · Zbl 1405.83064 |
| [43] | Hertog, T.; Maeda, K., J. High Energy Phys., 0407, 051 (2004) |
| [44] | Duff, M. J.; Liu, J. T., Nucl. Phys. B, 554, 237 (1999) · Zbl 0951.83060 |
| [45] | de Wit, B.; Nicolai, H., Nucl. Phys. B, 208, 323 (1982) |
| [46] | Dall’Agata, G.; Inverso, G.; Trigiante, M., Phys. Rev. Lett., 109, 201301 (2012) |
| [47] | Kodama, H.; Nozawa, M., J. High Energy Phys., 1301, 045 (2013) |
| [48] | Dall’Agata, G.; Inverso, G., Nucl. Phys. B, 859, 70 (2012) · Zbl 1246.83217 |
| [49] | Dall’Agata, G.; Inverso, G., Phys. Lett. B, 718, 1132 (2013) · Zbl 1332.83104 |
| [50] | Catino, F.; Dall’Agata, G.; Inverso, G.; Zwirner, F., J. High Energy Phys., 1309, 040 (2013) |
| [51] | Aldazabal, G.; Graña, M.; Marqués, D.; Rosabal, J. A., J. High Energy Phys., 1306, 046 (2013) |
| [52] | de Wit, B.; Samtleben, H.; Trigiante, M., J. High Energy Phys., 0706, 049 (2007) |
| [53] | Le Diffon, A.; Samtleben, H.; Trigiante, M., J. High Energy Phys., 1104, 079 (2011) |
| [54] | de Wit, B.; Samtleben, H.; Trigiante, M., J. High Energy Phys., 0509, 016 (2005) |
| [55] | Meessen, P.; Ortin, T.; Vaula, S., J. High Energy Phys., 1011, 072 (2010) |
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