×

On the supersymmetric solutions of D=3 half-maximal supergravities. (English) Zbl 1206.83151

Summary: We initiate a systematic study of the solutions of three-dimensional matter-coupled half-maximal \((N=8)\) supergravities which admit a Killing spinor. To this end we analyze in detail the invariant tensors built from spinor bilinears, a technique originally developed and applied in higher dimensions. This reveals an intriguing interplay with the scalar target space geometry \(SO(8,n)/(SO(8)\times SO(n))\). Another interesting feature of the three-dimensional case is the implementation of the duality between vector and scalar fields in this framework. For the ungauged theory with timelike Killing vector, we explicitly determine the scalar current and show that its integrability relation reduces to a covariant holomorphicity equation, for which we present a number of explicit solutions. For the case of a null Killing vector, we give the most general solution which is of pp-wave type.

MSC:

83E50 Supergravity

Software:

Cadabra
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Tod, K. P., All metrics admitting supercovariantly constant spinors, Phys. Lett. B, 121, 241-244 (1983)
[2] Tod, K. P., More on supercovariantly constant spinors, Class. Quant. Grav., 12, 1801-1820 (1995) · Zbl 0831.53070
[3] Gibbons, G. W.; Hull, C. M., A Bogomolny bound for general relativity and solitons in \(N = 2\) supergravity, Phys. Lett. B, 109, 190 (1982)
[4] Gauntlett, J. P.; Martelli, D.; Pakis, S.; Waldram, D., G-structures and wrapped NS5-branes, Commun. Math. Phys., 247, 421-445 (2004) · Zbl 1061.81058
[5] Gauntlett, J. P.; Gutowski, J. B.; Hull, C. M.; Pakis, S.; Reall, H. S., All supersymmetric solutions of minimal supergravity in five dimensions, Class. Quant. Grav., 20, 4587-4634 (2003) · Zbl 1045.83001
[6] Caldarelli, M. M.; Klemm, D., All supersymmetric solutions of \(N = 2, D = 4\) gauged supergravity, JHEP, 0309, 019 (2003)
[7] Meessen, P.; Ortin, T., The supersymmetric configurations of \(N = 2, d = 4\) supergravity coupled to vector supermultiplets, Nucl. Phys. B, 749, 291-324 (2006) · Zbl 1214.83047
[8] Hübscher, M.; Meessen, P.; Ortin, T., Supersymmetric solutions of \(N = 2, d = 4\) SUGRA: The whole ungauged shebang, Nucl. Phys. B, 759, 228-248 (2006) · Zbl 1116.83026
[9] Cacciatori, S. L.; Klemm, D.; Mansi, D. S.; Zorzan, E., All timelike supersymmetric solutions of \(N = 2, D = 4\) gauged supergravity coupled to Abelian vector multiplets, JHEP, 0805, 097 (2008)
[10] Klemm, D.; Zorzan, E., All null supersymmetric backgrounds of \(N = 2, D = 4\) gauged supergravity coupled to Abelian vector multiplets, Class. Quant. Grav., 26, 145018 (2009) · Zbl 1172.83023
[11] Hristov, K.; Looyestijn, H.; Vandoren, S., Maximally supersymmetric solutions of \(D = 4, N = 2\) gauged supergravity, JHEP, 0911, 115 (2009)
[12] Bellorin, J.; Ortin, T., All the supersymmetric configurations of \(N = 4, d = 4\) supergravity, Nucl. Phys. B, 726, 171-209 (2005) · Zbl 1113.83312
[13] Liu, J. T.; Mahato, M.; Vaman, D., Mapping the G-structures and supersymmetric vacua of five-dimensional \(N = 4\) supergravity, Class. Quant. Grav., 24, 1115-1144 (2007) · Zbl 1118.83015
[14] Cariglia, M.; Mac Conamhna, O. A.P., Timelike Killing spinors in seven dimensions, Phys. Rev. D, 70, 125009 (2004)
[15] Mac Conamhna, O. A.P., Refining G-structure classifications, Phys. Rev. D, 70, 105024 (2004)
[16] Marcus, N.; Schwarz, J. H., Three-dimensional supergravity theories, Nucl. Phys. B, 228, 145 (1983)
[17] Nicolai, H.; Samtleben, H., \(N = 8\) matter coupled \(AdS_3\) supergravities, Phys. Lett. B, 514, 165-172 (2001) · Zbl 0969.83548
[18] Förste, S.; Kehagias, A., Three-dimensional solitonic solutions, Nucl. Phys. B (Proc. Suppl.), 56B, 102-107 (1997) · Zbl 0957.81706
[19] Bakas, I.; Bourdeau, M.; Lopes Cardoso, G., Supersymmetric solutions in three-dimensional heterotic string theory, Nucl. Phys. B, 510, 103-138 (1998) · Zbl 0953.81083
[20] Bourdeau, M.; Lopes Cardoso, G., Finite energy solutions in three-dimensional heterotic string theory, Nucl. Phys. B, 522, 137-157 (1998) · Zbl 1047.81542
[21] Greene, B. R.; Shapere, A. D.; Vafa, C.; Yau, S.-T., Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B, 337, 1 (1990) · Zbl 0744.53045
[22] Sen, A., Strong-weak coupling duality in three-dimensional string theory, Nucl. Phys. B, 434, 179-209 (1995) · Zbl 1020.81802
[23] Berg, M.; Samtleben, H., An exact holographic RG flow between 2d conformal fixed points, JHEP, 0205, 006 (2002)
[24] Berg, M.; Hohm, O.; Samtleben, H., Holography of D-brane reconnection, JHEP, 0704, 013 (2007)
[25] Gava, E.; Karndumri, P.; Narain, K. S., \(AdS_3\) vacua and RG flows in three-dimensional gauged supergravities, JHEP, 1004, 117 (2010) · Zbl 1272.83082
[26] de Wit, B.; Herger, I.; Samtleben, H., Gauged locally supersymmetric \(D = 3\) nonlinear sigma models, Nucl. Phys. B, 671, 175-216 (2003) · Zbl 1058.81070
[27] Nicolai, H.; Samtleben, H., Kaluza-Klein supergravity on \(AdS_3 \times S^3\), JHEP, 0309, 036 (2003)
[28] Hohm, O.; Samtleben, H., Effective actions for massive Kaluza-Klein states on \(AdS_3 \times S^3 \times S^3\), JHEP, 0505, 027 (2005)
[29] N.S. Deger, H. Samtleben, Ö. Sarıoğlu, in preparation.; N.S. Deger, H. Samtleben, Ö. Sarıoğlu, in preparation.
[30] Kallosh, R.; Ortin, T., Killing spinor identities
[31] Bellorin, J.; Ortin, T., A note on simple applications of the Killing spinor identities, Phys. Lett. B, 616, 118-124 (2005) · Zbl 1247.53061
[32] Bellorin, J.; Ortin, T., Characterization of all the supersymmetric solutions of gauged \(N = 1, d = 5\) supergravity, JHEP, 0708, 096 (2007) · Zbl 1326.83079
[33] Hübscher, M.; Meessen, P.; Ortin, T.; Vaula, S., \(N = 2\) Einstein-Yang-Mills’s BPS solutions, JHEP, 0809, 099 (2008) · Zbl 1245.83079
[34] Schön, J.; Weidner, M., Gauged \(N = 4\) supergravities, JHEP, 0605, 034 (2006)
[35] C. Ellmer, Supersymmetrische Konfigurationen in \(N = 4D = 4\); C. Ellmer, Supersymmetrische Konfigurationen in \(N = 4D = 4\)
[36] Bergshoeff, E. A.; de Roo, M.; Hohm, O.; Roest, D., Multiple membranes from gauged supergravity, JHEP, 0808, 091 (2008)
[37] Bergshoeff, E. A.; Hohm, O.; Roest, D.; Samtleben, H.; Sezgin, E., The superconformal gaugings in three dimensions, JHEP, 0809, 101 (2008) · Zbl 1245.81081
[38] Bagger, J.; Lambert, N., Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D, 77, 065008 (2008)
[39] Gustavsson, A., Algebraic structures on parallel M2-branes, Nucl. Phys. B, 811, 66-76 (2009) · Zbl 1194.81205
[40] Jeon, I.; Kim, J.; Kim, N.; Kim, S.-W.; Park, J.-H., Classification of the BPS states in Bagger-Lambert theory, JHEP, 0807, 056 (2008)
[41] Jeon, I.; Kim, J.; Lee, B.-H.; Park, J.-H.; Kim, N., M-brane bound states and the supersymmetry of BPS solutions in the Bagger-Lambert theory, Int. J. Mod. Phys. A, 24, 5779-5801 (2009) · Zbl 1179.81135
[42] Peeters, K., A field-theory motivated approach to symbolic computer algebra, Comput. Phys. Commun., 176, 550-558 (2007) · Zbl 1196.68333
[43] Peeters, K., Introducing Cadabra: A symbolic computer algebra system for field theory problems · Zbl 1196.68333
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.