Abstract
We construct explicit consistent Kaluza–Klein reductions of type IIB supergravity on HK 4 ×S 1, where HK 4 is an arbitrary four-dimensional hyper-Kähler manifold, and on SE 5, an arbitrary five-dimensional Sasaki–Einstein manifold. In the former case we obtain the bosonic action of D = 5 N = 4 (ungauged) supergravity coupled to two vector multiplets. For the SE 5 case we extend a known reduction, which leads to minimal D = 5 N = 2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE 5. We show that the resulting D = 5 action is also consistent with N = 4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS 5 vacuum, which uplifts to the class of supersymmetric AdS 5 × SE 5 solutions, that spontaneously breaks N = 4 to N = 2, and also a non-supersymmetric AdS 5 vacuum which uplifts to a class of solutions first found by Romans.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Buchel and J.T. Liu, Gauged supergravity from type IIB string theory on Y (p, q) manifolds, Nucl. Phys. B 771 (2007) 93 [hep-th/0608002] [SPIRES].
J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [SPIRES].
B. de Wit and H. Nicolai, The Consistency of the S 7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [SPIRES].
M. Cvetič et al., Embedding AdS black holes in ten and eleven dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [SPIRES].
H. Lü, C.N. Pope and T.A. Tran, Five-dimensional N = 4, SU(2) × U(1) gauged supergravity from type IIB, Phys. Lett. B 475 (2000) 261 [hep-th/9909203] [SPIRES].
M. Cvetič, H. Lü, C.N. Pope, A. Sadrzadeh and T.A. Tran, Consistent SO(6) reduction of type IIB supergravity on S 5, Nucl. Phys. B 586 (2000) 275 [hep-th/0003103] [SPIRES].
A. Khavaev, K. Pilch and N.P. Warner, New vacua of gauged N = 8 supergravity in five dimensions, Phys. Lett. B 487 (2000) 14 [hep-th/9812035] [SPIRES].
J.P. Gauntlett, E. O Colgain and O. Varela, Properties of some conformal field theories with M-theory duals, JHEP 02 (2007) 049 [hep-th/0611219] [SPIRES].
J.P. Gauntlett and O. Varela, D = 5 SU(2) × U(1) Gauged Supergravity from D = 11 Supergravity, JHEP 02 (2008) 083 [arXiv:0712.3560] [SPIRES].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 1 1D supergravity on AdS 7 × S 4 and self-duality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [SPIRES].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS 7 × S 4 reduction and the origin of self-duality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [SPIRES].
J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza–Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [SPIRES].
For a review see M. Graña, Flux compactifications in string theory: A comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [SPIRES].
E. O’ Colgain, O. Varela and H. Yavartanoo, Non-relativistic M-theory solutions based on Kähler- Einstein spaces, JHEP 07 (2009) 081 [arXiv:0906.0261] [SPIRES].
G. Dall’Agata, C. Herrmann and M. Zagermann, General matter coupled N = 4 gauged supergravity in five dimensions, Nucl. Phys. B 612 (2001) 123 [hep-th/0103106] [SPIRES].
J. Schon and M. Weidner, Gauged N = 4 supergravities, JHEP 05 (2006) 034 [hep-th/0602024] [SPIRES].
H. Lü, C.N. Pope and K.S. Stelle, M-theory/heterotic duality: A Kaluza-Klein perspective, Nucl. Phys. B 548 (1999) 87 [hep-th/9810159] [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].
L.J. Romans, New Compactifications Of Chiral N = 2 D = 10 Supergravity, Phys. Lett. B 153 (1985) 392 [SPIRES].
C.N. Pope and N.P. Warner, An SU(4) Invariant Compactification Of D = 11 Supergravity On A Stretched Seven Sphere, Phys. Lett. B 150 (1985) 352 [SPIRES].
C.N. Pope and N.P. Warner, Two New Classes Of Compactifications Of D = 11 Supergravity, Class. Quant. Grav. 2 (1985) L1 [SPIRES].
N. Halmagyi, K. Pilch and N. Warner, private communication.
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [1003.4283] [SPIRES].
J.T. Liu, P. Szepietowski and Z. Zhao, Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds, 1003.5374 [SPIRES].
K. Skenderis, M. Taylor and D. Tsimpis, A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, 1003.5657 [SPIRES].
J.H. Schwarz, Covariant Field Equations of Chiral N = 2 D = 10 Supergravity, Nucl. Phys. B 226 (1983) 269 [SPIRES].
P.S. Howe and P.C. West, The Complete N = 2, D = 10 Supergravity, Nucl. Phys. B 238 (1984) 181 [SPIRES].
M. Awada and P.K. Townsend, N = 4 Maxwell-Einstein Supergravity In Five-Dimensions And Its SU(2) Gauging, Nucl. Phys. B 255 (1985) 617 [SPIRES].
L. Andrianopoli, R. D’Auria, S. Ferrara, P. Fré and M. Trigiante, R-R scalars, U-duality and solvable Lie algebras, Nucl. Phys. B 496 (1997) 617 [hep-th/9611014] [SPIRES].
L. Andrianopoli et al., Solvable Lie algebras in type IIA, type IIB and M theories, Nucl. Phys. B 493 (1997) 249 [hep-th/9612202] [SPIRES].
B. de Wit, H. Samtleben and M. Trigiante, On Lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [SPIRES].
H. Samtleben, Lectures on Gauged Supergravity and Flux Compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [SPIRES].
J.A. Minahan and R.C. Warner, Stuckelberg Revisited, UFIFT preprint HEP-89-15 (1989) [SPIRES].
P. K. Townsend, K. Pilch and P. van Nieuwenhuizen, Selfduality In Odd Dimensions, Phys. Lett. 136B (1984) 38 [Addendum-ibid. 137B (1984) 443] [SPIRES].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS 5 × T 11 : Predictions on N = 1 SCFT’s, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [SPIRES].
A. Ceresole, G. Dall’Agata and R. D’Auria, KK spectroscopy of type IIB supergravity on AdS 5 × T 11, JHEP 11 (1999) 009 [hep-th/9907216] [SPIRES].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The Mass Spectrum of Chiral N = 2 D = 10 Supergravity on S 5, Phys. Rev. D 32 (1985) 389 [SPIRES].
M. Günaydin and N. Marcus, The Spectrum of the S 5 Compactification of the Chiral N = 2, D = 10 Supergravity and the Unitary Supermultiplets of U(2, 2/4), Class. Quant. Grav. 2 (1985) L11 [SPIRES].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non- relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [SPIRES].
T.T. Tsikas, Consistent Truncations Of Chiral N = 2 D = 10 Supergravity On The Round Five Sphere, Class. Quant. Grav. 3 (1986) 733 [SPIRES].
M.S. Bremer, M.J. Duff, H. Lü, C.N. Pope and K.S. Stelle, Instanton cosmology and domain walls from M-theory and string theory, Nucl. Phys. B 543 (1999) 321 [hep-th/9807051] [SPIRES].
J.T. Liu and H. Sati, Breathing mode compactifications and supersymmetry of the brane-world, Nucl. Phys. B 605 (2001) 116 [hep-th/0009184] [SPIRES].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [SPIRES].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [SPIRES].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [SPIRES].
J.T. Liu and C.N. Pope, Inconsistency of Breathing Mode Extensions of Maximal Five-Dimensional Supergravity Embedding, 1005.4654 [SPIRES].
M. Billó, D. Fabbri, P. Fré, P. Merlatti and A. Zaffaroni, Shadow multiplets in AdS 4/CFT 3 and the super-Higgs mechanism, Nucl. Phys. B 591 (2000) 139 [hep-th/0005220] [SPIRES].
C.P. Boyer and K. Galicki, 3-Sasakian Manifolds, Surveys Diff. Geom. 7 (1999) 123 [hep-th/9810250] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gauntlett, J.P., Varela, O. Universal Kaluza-Klein reductions of type IIB to N = 4 supergravity in five dimensions. J. High Energ. Phys. 2010, 81 (2010). https://doi.org/10.1007/JHEP06(2010)081
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2010)081