Abstract
General Lagrangians are constructed for N = 2 conformal supergravity theories in four space-time dimensions involving gauge groups with abelian and/or non-abelian electric and magnetic charges. The charges are encoded in the gauge group embedding tensor. The scalar potential induced by the gauge interactions is quadratic in this tensor, and, when the embedding tensor is treated as a spurionic quantity, it is formally covariant with respect to electric/magnetic duality. This work establishes a general framework for studying any deformation induced by gauge interactions of matter-coupled N = 2 supergravity theories. As an application, full and residual supersymmetry realizations in maximally symmetric space-times are reviewed. Furthermore, a general classification is presented of supersymmetric solutions in AdS2 × S 2 space-times. As it turns out, these solutions allow either eight or four supersymmetries. With four supersymmetries, the spinorial parameters are Killing spinors of AdS2 that are constant on S 2, so that they carry no spin, while the bosonic background is rotationally invariant.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. de Wit, Electric magnetic dualities in supergravity, Nucl. Phys. Proc. Suppl. 101 (2001) 154 [hep-th/0103086] [SPIRES].
L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [SPIRES].
B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [SPIRES].
B. de Wit, J. van Holten and A. Van Proeyen, Structure of N = 2 supergravity, Nucl. Phys. B 184 (1981) 77 [Erratum ibid. B 222 (1983) 516] [SPIRES].
B. de Wit and A. Van Proeyen, Potentials and symmetries of general gauged N = 2 supergravity: Yang-Mills models, Nucl. Phys. B 245 (1984) 89 [SPIRES].
B. de Wit, P. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [SPIRES].
M. de Vroome and B. de Wit, Lagrangians with electric and magnetic charges of N = 2 supersymmetric gauge theories, JHEP 08 (2007) 064 [arXiv:0707.2717] [SPIRES].
J. Louis and A. Micu, Type 2 theories compactified on Calabi-Yau threefolds in the presence of background fluxes, Nucl. Phys. B 635 (2002) 395 [hep-th/0202168] [SPIRES].
G. Dall’Agata, R. D’Auria, L. Sommovigo and S. Vaula, D = 4, N = 2 gauged supergravity in the presence of tensor multiplets, Nucl. Phys. B 682 (2004) 243 [hep-th/0312210] [SPIRES].
L. Sommovigo and S. Vaula, D = 4, N = 2 supergravity with abelian electric and magnetic charge, Phys. Lett. B 602 (2004) 130 [hep-th/0407205] [SPIRES].
R. D’Auria, L. Sommovigo and S. Vaula, N = 2 supergravity Lagrangian coupled to tensor multiplets with electric and magnetic fluxes, JHEP 11 (2004) 028 [hep-th/0409097] [SPIRES].
J. Schon and M. Weidner, Gauged N = 4 supergravities, JHEP 05 (2006) 034 [hep-th/0602024] [SPIRES].
B. de Wit, H. Samtleben and M. Trigiante, The maximal D = 4 supergravities, JHEP 06 (2007) 049 [arXiv:0705.2101] [SPIRES].
J. Hartong, M. Hubscher and T. Ortín, The supersymmetric tensor hierarchy of N = 1, d = 4 supergravity, JHEP 06 (2009) 090 [arXiv:0903.0509] [SPIRES].
I. Antoniadis, H. Partouche and T. Taylor, Spontaneous breaking of N = 2 global supersymmetry, Phys. Lett. B 372 (1996) 83 [hep-th/9512006] [SPIRES].
K. Behrndt, G. Lopes Cardoso and D. Lüst, Curved BPS domain wall solutions in four-dimensional N = 2 supergravity, Nucl. Phys. B 607 (2001) 391 [hep-th/0102128] [SPIRES].
M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [SPIRES].
J. Louis, P. Smyth and H. Triendl, Spontaneous N = 2 to N = 1 supersymmetry breaking in supergravity and type II string theory, JHEP 02 (2010) 103 [arXiv:0911.5077] [SPIRES].
J. Louis, P. Smyth and H. Triendl, The N = 1 low-energy effective action of spontaneously broken N = 2 supergravities, JHEP 10 (2010) 017 [arXiv:1008.1214] [SPIRES].
S. Cecotti, L. Girardello and M. Porrati, Two into one won’t go, Phys. Lett. B 145 (1984) 61 [SPIRES].
S. Cecotti, L. Girardello and M. Porrati, An exceptional N = 2 supergravity with flat potential and partial superHiggs, Phys. Lett. B 168 (1986) 83 [SPIRES].
S. Ferrara, L. Girardello and M. Porrati, Spontaneous breaking of N = 2 to N = 1 in rigid and local supersymmetric theories, Phys. Lett. B 376 (1996) 275 [hep-th/9512180] [SPIRES].
S. Ferrara, L. Girardello and M. Porrati, Minimal Higgs branch for the breaking of half of the supersymmetries in N = 2 supergravity, Phys. Lett. B 366 (1996) 155 [hep-th/9510074] [SPIRES].
P. Fré, L. Girardello, I. Pesando and M. Trigiante, Spontaneous N = 2 → N = 1 local supersymmetry breaking with surviving compact gauge group, Nucl. Phys. B 493 (1997) 231 [hep-th/9607032] [SPIRES].
K. Hristov, H. Looyestijn and S. Vandoren, Maximally supersymmetric solutions of D = 4 N = 2 gauged supergravity, JHEP 11 (2009) 115 [arXiv:0909.1743] [SPIRES].
P. Hasenfratz and G. ’t Hooft, A fermion-boson puzzle in a gauge theory, Phys. Rev. Lett. 36 (1976) 1119 [SPIRES].
G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [SPIRES].
K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [SPIRES].
B. de Wit, S. Katmadas and M. van Zalk, New supersymmetric higher-derivative couplings: full N = 2 superspace does not count!, JHEP 01 (2011) 007 [arXiv:1010.2150] [SPIRES].
B. de Wit, P.G. Lauwers, R. Philippe, S.Q. Su and A. Van Proeyen, Gauge and matter fields coupled to N = 2 supergravity, Phys. Lett. B 134 (1984) 37 [SPIRES].
S. Cecotti, S. Ferrara and L. Girardello, Geometry of type II superstrings and the moduli of superconformal field theories, Int. J. Mod. Phys. A 4 (1989) 2475 [SPIRES].
B. de Wit, B. Kleijn and S. Vandoren, Superconformal hypermultiplets, Nucl. Phys. B 568 (2000) 475 [hep-th/9909228] [SPIRES].
B. de Wit, B. Kleijn and S. Vandoren, Rigid N = 2 superconformal hypermultiplets, hep-th/9808160 [SPIRES].
G. Gibbons and P. Rychenkova, Cones, tri-Sasakian structures and superconformal invariance, Phys. Lett. B 443 (1998) 138 [hep-th/9809158] [SPIRES].
B. de Wit, M. Roček and S. Vandoren, Gauging isometries on hyper-Kähler cones and quaternion Kähler manifolds, Phys. Lett. B 511 (2001) 302 [hep-th/0104215] [SPIRES].
A. Swann, HyperKähler and quaternionic Kähler geometry, Math. Ann. 289 (1991) 421.
B. de Wit and F. Saueressig, Off-shell N = 2 tensor supermultiplets, JHEP 09 (2006) 062 [hep-th/0606148] [SPIRES].
B. de Wit, H. Samtleben and M. Trigiante, Gauging maximal supergravities, Fortsch. Phys. 52 (2004) 489 [hep-th/0311225] [SPIRES].
B. de Wit and H. Samtleben, Gauged maximal supergravities and hierarchies of nonAbelian vector-tensor systems, Fortsch. Phys. 53 (2005) 442 [hep-th/0501243] [SPIRES].
B. de Wit, H. Nicolai and H. Samtleben, Gauged supergravities, tensor hierarchies and M-theory, JHEP 02 (2008) 044 [arXiv:0801.1294] [SPIRES].
R. D’Auria, S. Ferrara and P. Fré, Special and quaternionic isometries: General couplings in N = 2 supergravity and the scalar potential, Nucl. Phys. B 359 (1991) 705 [SPIRES].
G. LopesCardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [SPIRES].
L. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [SPIRES].
M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [SPIRES].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1107.3305
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
de Wit, B., van Zalk, M. Electric and magnetic charges in N = 2 conformal supergravity theories. J. High Energ. Phys. 2011, 50 (2011). https://doi.org/10.1007/JHEP10(2011)050
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2011)050