Abstract
We find infinite families of supersymmetric solutions of four dimensional, \( \mathcal{N} = 2 \) gauged supergravity with Lifshitz, Schrödinger and also AdS symmetries. We focus on the canonical example of a single hypermultiplet and a single vector multiplet and find that the spectrum of solutions depends crucially on whether the gaugings are electric or magnetic but to a far milder extent on the strength of the gaugings. For purely electric or purely magnetic gaugings we generically find Lifshitz solutions, while for a mixed gauging we find Schrödinger and AdS solutions. For some of the gaugings the theory has a known lift to string/M-theory thus giving a higher dimensional embedding of our solutions.
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References
J.M. Maldacena, The large- \( \mathcal{N} \) limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].
D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].
P. Koroteev and M. Libanov, On existence of self-tuning solutions in static braneworlds without singularities, JHEP 02 (2008) 104 [arXiv:0712.1136] [SPIRES].
C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [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].
A. Adams, K. Balasubramanian and J. McGreevy, Hot spacetimes for cold atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [SPIRES].
S.A. Hartnoll and K. Yoshida, Families of IIB duals for nonrelativistic CFTs, JHEP 12 (2008) 071 [arXiv:0810.0298] [SPIRES].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [SPIRES].
A. Donos and J.P. Gauntlett, Supersymmetric solutions for non-relativistic holography, JHEP 03 (2009) 138 [arXiv:0901.0818] [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].
N. Bobev and A. Kundu, Deformations of holographic duals to non-relativistic CFTs, JHEP 07 (2009) 098 [arXiv:0904.2873] [SPIRES].
N. Bobev, A. Kundu and K. Pilch, Supersymmetric IIB solutions with Schrödinger symmetry, JHEP 07 (2009) 107 [arXiv:0905.0673] [SPIRES].
A. Donos and J.P. Gauntlett, Solutions of type IIB and D = 11 supergravity with Schrödinger(z) symmetry, JHEP 07 (2009) 042 [arXiv:0905.1098] [SPIRES].
A. Donos and J.P. Gauntlett, Schrödinger invariant solutions of type IIB with enhanced supersymmetry, JHEP 10 (2009) 073 [arXiv:0907.1761] [SPIRES].
A. Donos and J.P. Gauntlett, Lifshitz solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [SPIRES].
A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [SPIRES].
J. Jeong, H.-C. Kim, S. Lee, E. O Colgain and H. Yavartanoo, Schrödinger invariant solutions of M-theory with enhanced supersymmetry, JHEP 03 (2010) 034 [arXiv:0911.5281] [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].
H. Ooguri and C.-S. Park, Supersymmetric non-relativistic geometries in M-theory, Nucl. Phys. B 824 (2010) 136 [arXiv:0905.1954] [SPIRES].
E. O Colgain and H. Yavartanoo, NR CFT 3 duals in M-theory, JHEP 09 (2009) 002 [arXiv:0904.0588] [SPIRES].
K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [SPIRES].
P. Kraus and E. Perlmutter, Universality and exactness of Schrödinger geometries in string and M-theory, JHEP 05 (2011) 045 [arXiv:1102.1727] [SPIRES].
J. Blaback, U.H. Danielsson and T. Van Riet, Lifshitz backgrounds from 10 d supergravity, JHEP 02 (2010) 095 [arXiv:1001.4945] [SPIRES].
R. Gregory, S.L. Parameswaran, G. Tasinato and I. Zavala, Lifshitz solutions in supergravity and string theory, JHEP 12 (2010) 047 [arXiv:1009.3445] [SPIRES].
N. Bobev and B.C. van Rees, Schrödinger deformations of AdS 3 × S 3, arXiv:1102.2877 [SPIRES].
D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [SPIRES].
B. de Wit and H. Nicolai, \( \mathcal{N} = 8 \) supergravity, Nucl. Phys. B 208 (1982) 323 [SPIRES].
M. Günaydin, L.J. Romans and N.P. Warner, Gauged \( \mathcal{N} = 8 \) supergravity in five-dimensions, Phys. Lett. B 154 (1985) 268 [SPIRES].
K. Pilch, P. van Nieuwenhuizen and P.K. Townsend, Compactification of D = 11 supergravity on S 4 (or 11 = 7 + 4, too), Nucl. Phys. B 242 (1984) 377 [SPIRES].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear KK reduction of 11 d supergravity on AdS 7 × S 4 and self-duality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [SPIRES].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, Novel local CFT and exact results on perturbations of \( \mathcal{N} = 4 \) super Yang-Mills from AdS dynamics, JHEP 12 (1998) 022 [hep-th/9810126] [SPIRES].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c-theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [SPIRES].
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].
T. House and E. Palti, Effective action of (massive) IIA on manifolds with SU(3) structure, Phys. Rev. D 72 (2005) 026004 [hep-th/0505177] [SPIRES].
A.-K. Kashani-Poor, Nearly Kähler reduction, JHEP 11 (2007) 026 [arXiv:0709.4482] [SPIRES].
D. Cassani and A.-K. Kashani-Poor, Exploiting \( \mathcal{N} = 2 \) in consistent coset reductions of type IIA, Nucl. Phys. B 817 (2009) 25 [arXiv:0901.4251] [SPIRES].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity instabilities of non-supersymmetric quantum critical points, Class. Quant. Grav. 27 (2010) 235013 [arXiv:1006.2546] [SPIRES].
K. Behrndt and M. Cvetič, Gauging of \( \mathcal{N} = 2 \) supergravity hypermultiplet and novel renormalization group flows, Nucl. Phys. B 609 (2001) 183 [hep-th/0101007] [SPIRES].
A. Ceresole, G. Dall’Agata, R. Kallosh and A. Van Proeyen, Hypermultiplets, domain walls and supersymmetric attractors, Phys. Rev. D 64 (2001) 104006 [hep-th/0104056] [SPIRES].
K. Hristov, H. Looyestijn and S. Vandoren, BPS black holes in \( \mathcal{N} = 2 \) D =4 gauged supergravities, JHEP 08 (2010) 103 [arXiv:1005.3650] [SPIRES].
S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009) 105007 [arXiv:0908.1972] [SPIRES].
N.P. Warner, Some new extrema of the scalar potential of gauged \( \mathcal{N} = 8 \) supergravity, Phys. Lett. B 128 (1983) 169 [SPIRES].
L. Andrianopoli et al., General matter coupled \( \mathcal{N} = 2 \) supergravity, Nucl. Phys. B 476 (1996) 397 [hep-th/9603004] [SPIRES].
L. Andrianopoli et al., \( \mathcal{N} = 2 \) supergravity and \( \mathcal{N} = 2 \) 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].
S. Ferrara, L. Girardello and M. Porrati, Spontaneous breaking of \( \mathcal{N} = 2 \) to \( \mathcal{N} = 1 \) in rigid and local supersymmetric theories, Phys. Lett. B 376 (1996) 275 [hep-th/9512180] [SPIRES].
L. Sommovigo and S. Vaula, D = 4, \( \mathcal{N} = 2 \) supergravity with Abelian electric and magnetic charge, Phys. Lett. B 602 (2004) 130 [hep-th/0407205] [SPIRES].
G. Dall’Agata, R. D’Auria, L. Sommovigo and S. Vaula, D = 4, \( \mathcal{N} = 2 \) gauged supergravity in the presence of tensor multiplets, Nucl. Phys. B 682 (2004) 243 [hep-th/0312210] [SPIRES].
B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [SPIRES].
D. Cassani, S. Ferrara, A. Marrani, J.F. Morales and H. Samtleben, A special road to AdS vacua, JHEP 02 (2010) 027 [arXiv:0911.2708] [SPIRES].
G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in \( \mathcal{N} = 2 \) U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [SPIRES].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Holographic, \( \mathcal{N} = 1 \) supersymmetric RG flows on M2 branes, JHEP 09 (2009) 043 [arXiv:0901.2736] [SPIRES].
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [SPIRES].
J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to \( \mathcal{N} = 4 \) supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [SPIRES].
J.T. Liu, P. Szepietowski and Z. Zhao, Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds, Phys. Rev. D 81 (2010) 124028 [arXiv:1003.5374] [SPIRES].
K. Skenderis, M. Taylor and D. Tsimpis, A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, JHEP 06 (2010) 025 [arXiv:1003.5657] [SPIRES].
R. Britto-Pacumio, A. Strominger and A. Volovich, Holography for coset spaces, JHEP 11 (1999) 013 [hep-th/9905211] [SPIRES].
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Halmagyi, N., Petrini, M. & Zaffaroni, A. Non-relativistic solutions of \( \mathcal{N} = 2 \) gauged supergravity. J. High Energ. Phys. 2011, 41 (2011). https://doi.org/10.1007/JHEP08(2011)041
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DOI: https://doi.org/10.1007/JHEP08(2011)041