An eight-dimensional approach to \(G_2\) manifolds. (English) Zbl 0995.83060
Summary: We develop a systematic approach to \(G_2\) holonomy manifolds with an \(\text{SU}(2)\times\text{SU}(2)\) isometry using maximal eight-dimensional gauged supergravity to describe D6-branes wrapped on deformed three-spheres. A quite general metric ansatz that generalizes the celebrated Bryant-Salamon metric involves nine functions. We show that only six of them are independent ones and derive the general first order system of differential equations that they obey. As a byproduct of our analysis, we generalize the notion of the twist that relates the spin and gauge connections in a way that involves non-trivially the scalar fields.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
References:
| [1] | Vafa, C., J. Math. Phys., 42, 2798 (2001) · Zbl 1060.81594 |
| [2] | Acharya, B. S. |
| [3] | Atiyah, M.; Maldacena, J.; Vafa, C., J. Math. Phys., 42, 3209 (2001) · Zbl 1061.81056 |
| [4] | Cachazo, F.; Intriligator, K. A.; Vafa, C., Nucl. Phys. B, 603, 3 (2001) · Zbl 0983.81050 |
| [5] | Gomis, J., Nucl. Phys. B, 606, 3 (2001) · Zbl 0971.81112 |
| [6] | Cvetič, M.; Gibbons, G. W.; Lu, H.; Pope, C. N., Nucl. Phys. B, 620, 29 (2002) · Zbl 1037.53032 |
| [7] | Kachru, S.; McGreevy, J., JHEP, 0106, 027 (2001) |
| [8] | Edelstein, J. D.; Oh, K.; Tatar, R., JHEP, 0105, 009 (2001) |
| [9] | Gutowski, J.; Papadopoulos, G., Nucl. Phys. B, 615, 237 (2001) · Zbl 0974.83048 |
| [10] | Kaste, P.; Kehagias, A.; Partouche, H., JHEP, 0105, 058 (2001) |
| [11] | Dasgupta, K.; Oh, K.; Tatar, R., Nucl. Phys. B, 610, 331 (2001) · Zbl 0971.81118 |
| [12] | Brandhuber, A.; Gomis, J.; Gubser, S. S.; Gukov, S., Nucl. Phys. B, 611, 179 (2001) · Zbl 0971.81071 |
| [13] | Atiyah, M.; Witten, E. |
| [14] | Witten, E. |
| [15] | Kanno, H.; Yasui, Y. |
| [16] | Cvetič, M.; Gibbons, G. W.; Lu, H.; Pope, C. N. |
| [17] | Gukov, S.; Sparks, J., Nucl. Phys. B, 625, 3 (2002) · Zbl 0989.83047 |
| [18] | Majumder, J., JHEP, 0201, 048 (2002) |
| [19] | Acharya, B.; Witten, E. |
| [20] | Giveon, A.; Kehagias, A.; Partouche, H., JHEP, 0112, 021 (2001) |
| [21] | Blumenhagen, R.; Braun, V., JHEP, 0112, 013 (2001) |
| [22] | Ferretti, G.; Salomonson, P.; Tsimpis, D., JHEP, 0203, 004 (2002) |
| [23] | Cvetič, M.; Gibbons, G. W.; Lu, H.; Pope, C. N. |
| [24] | Curio, G.; Kors, B.; Lust, D. |
| [25] | Bilal, A.; Derendinger, J. P.; Sfetsos, K., Nucl. Phys. B, 628, 112 (2002) · Zbl 0992.83073 |
| [26] | Oh, K.; Tatar, R. |
| [27] | Cvetič, M.; Gibbons, G. W.; Lu, H.; Pope, C. N., Phys. Rev. Lett., 88, 121602 (2002) |
| [28] | Brandhuber, A. |
| [29] | Cvetič, M.; Gibbons, G. W.; Lu, H.; Pope, C. N. |
| [30] | Hartnoll, S. A. |
| [31] | Acharya, B.; de la Ossa, X.; Gukov, S. |
| [32] | Maldacena, J.; Núnez, C., Phys. Rev. Lett., 86, 588 (2001) |
| [33] | Acharya, B.; Gauntlett, J. P.; Kim, N., Phys. Rev. D, 63, 106003 (2001) |
| [34] | Nieder, H.; Oz, Y., JHEP, 0103, 008 (2001) |
| [35] | Gauntlett, J. P.; Kim, N.; Waldram, D., Phys. Rev. D, 63, 126001 (2001) |
| [36] | Núnez, C.; Park, I. Y.; Schvellinger, M.; Tran, T. A., JHEP, 0104, 025 (2001) |
| [37] | Edelstein, J. D.; Núnez, C., JHEP, 0104, 028 (2001) |
| [38] | Schvellinger, M.; Tran, T. A., JHEP, 0106, 025 (2001) |
| [39] | Maldacena, J.; Nastase, H., JHEP, 0109, 024 (2001) |
| [40] | Gauntlett, J. P.; Kim, N.; Pakis, S.; Waldram, D., Phys. Rev. D, 65, 026003 (2002) |
| [41] | Hernández, R., Phys. Lett. B, 521, 371 (2001) · Zbl 1020.83030 |
| [42] | Bigazzi, F.; Cotrone, A. L.; Zaffaroni, A., Phys. Lett. B, 519, 269 (2001) · Zbl 0972.81109 |
| [43] | Gomis, J.; Mateos, T., Phys. Lett. B, 524, 170 (2002) · Zbl 0981.83051 |
| [44] | Gauntlett, J. P.; Kim, N., Phys. Rev. D, 65, 086003 (2002) |
| [45] | Gomis, J.; Russo, J. G., JHEP, 0110, 028 (2001) |
| [46] | Gauntlett, J. P.; Kim, N. W.; Martelli, D.; Waldram, D., JHEP, 0111, 018 (2001) |
| [47] | Gomis, J., Nucl. Phys. B, 624, 181 (2002) · Zbl 0985.81064 |
| [48] | Di Vecchia, P.; Enger, H.; Imeroni, E.; Lozano-Tellechea, E. |
| [49] | Gibbons, G. W.; Page, D. N.; Pope, C. N., Commun. Math. Phys., 127, 529 (1990) · Zbl 0699.53053 |
| [50] | Salam, A.; Sezgin, E., Nucl. Phys. B, 258, 284 (1985) |
| [51] | Kallosh, R.; Kumar, J., Phys. Rev. D, 56, 4934 (1997) |
| [52] | Belinsky, V. A.; Gibbons, G. W.; Page, D. N.; Pope, C. N., Phys. Lett. B, 76, 433 (1978) |
| [53] | Sfetsos, K. |
| [54] | Acharya, B. S.; O’Loughlin, M., Phys. Rev. D, 55, 4521 (1997) |
| [55] | Floratos, E. G.; Kehagias, A., Phys. Lett. B, 427, 283 (1998) · Zbl 1355.53021 |
| [56] | Brecher, D.; Perry, M. J., Nucl. Phys. B, 566, 151 (2000) · Zbl 0953.83041 |
| [57] | Gray, A., Math. Z., 123, 290 (1971) · Zbl 0222.53043 |
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