Abstract
Bianchi attractors are homogeneous but anisotropic extremal black brane horizons. We study the AdS 3 × ℍ2 solution which is a special case of Bianchi type III in a U(1) R gauged supergravity. For a wide range of values for certain free parameters in gauged supergravity, there exist a large class of solutions that satisfy conditions for the attractor mechanism to hold. We investigate the response of the solution against linearized fluctuations of the scalar field. The sufficient conditions for the attractor mechanism ensure that there exist a solution for the scalar fluctuation which dies out at the horizon. Furthermore, we solve for the gauge field and metric fluctuations that are sourced by scalar fluctuations and show that they are well behaved near the horizon. Thus, we have an example of a stable Bianchi attractor in gauged supergravity. We also analyze the Killing spinor equations of gauged supergravity in the background of our solution. We find that a radial Killing spinor consistent with the Bianchi III symmetry breaks supersymmetry.
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O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
S. Sachdev, Quantum phase transitions, Wiley Online Library (2007).
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
S. Sachdev, What can gauge-gravity duality teach us about condensed matter physics?, Ann. Rev. Condensed Matter Phys. 3 (2012) 9 [arXiv:1108.1197] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].
K. Goldstein et al., Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
S.S. Pal, Anisotropic gravity solutions in AdS/CMT, arXiv:0901.0599 [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
E. Perlmutter, Domain Wall Holography for Finite Temperature Scaling Solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
E. Perlmutter, Hyperscaling violation from supergravity, JHEP 06 (2012) 165 [arXiv:1205.0242] [INSPIRE].
K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [INSPIRE].
A. Donos and J.P. Gauntlett, Lifshitz Solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].
R. Gregory, S.L. Parameswaran, G. Tasinato and I. Zavala, Lifshitz solutions in supergravity and string theory, JHEP 12 (2010) 047 [arXiv:1009.3445] [INSPIRE].
K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].
P. Dey and S. Roy, Lifshitz-like space-time from intersecting branes in string/M theory, JHEP 06 (2012) 129 [arXiv:1203.5381] [INSPIRE].
P. Dey and S. Roy, Intersecting D-branes and Lifshitz-like space-time, Phys. Rev. D 86 (2012) 066009 [arXiv:1204.4858] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].
A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett. 108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].
N. Iizuka et al., Bianchi Attractors: A Classification of Extremal Black Brane Geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
N. Iizuka et al., Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes and a Classification for the Homogeneous Case, JHEP 03 (2013) 126 [arXiv:1212.1948] [INSPIRE].
A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].
S. Cremonini and A. Sinkovics, Spatially Modulated Instabilities of Geometries with Hyperscaling Violation, JHEP 01 (2014) 099 [arXiv:1212.4172] [INSPIRE].
J. Erdmenger, X.-H. Ge and D.-W. Pang, Striped phases in the holographic insulator/superconductor transition, JHEP 11 (2013) 027 [arXiv:1307.4609] [INSPIRE].
N. Iizuka, A. Ishibashi and K. Maeda, Can a stationary Bianchi black brane have momentum along the direction with no translational symmetry?, JHEP 06 (2014) 064 [arXiv:1403.0752] [INSPIRE].
L. Landau and D. Lifshitz, The classical theory of fields, Teor. Fizika, Pergamon Press (1975).
M. Ryan and L. Shepley, Homogeneous Relativistic Cosmologies, Princeton Series in Physics. Princeton University Press (1975).
S. Kachru, N. Kundu, A. Saha, R. Samanta and S.P. Trivedi, Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes, JHEP 03 (2014) 074 [arXiv:1310.5740] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [INSPIRE].
A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [INSPIRE].
S. Bellucci, S. Ferrara, R. Kallosh and A. Marrani, Extremal Black Hole and Flux Vacua Attractors, Lect. Notes Phys. 755 (2008) 115 [arXiv:0711.4547] [INSPIRE].
S. Ferrara, K. Hayakawa and A. Marrani, Lectures on Attractors and Black Holes, Fortsch. Phys. 56 (2008) 993 [arXiv:0805.2498] [INSPIRE].
S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [INSPIRE].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
K. Goldstein, N. Iizuka, R.P. Jena and S.P. Trivedi, Non-supersymmetric attractors, Phys. Rev. D 72 (2005) 124021 [hep-th/0507096] [INSPIRE].
N. Halmagyi, BPS Black Hole Horizons in N = 2 Gauged Supergravity, JHEP 02 (2014) 051 [arXiv:1308.1439] [INSPIRE].
S. Barisch-Dick, G. Lopes Cardoso, M. Haack and S. Nampuri, Extremal black brane solutions in five-dimensional gauged supergravity, JHEP 02 (2013) 103 [arXiv:1211.0832] [INSPIRE].
D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry, JHEP 01 (2013) 053 [arXiv:1207.2679] [INSPIRE].
S. Barisch, G. Lopes Cardoso, M. Haack, S. Nampuri and N.A. Obers, Nernst branes in gauged supergravity, JHEP 11 (2011) 090 [arXiv:1108.0296] [INSPIRE].
S. Kachru, R. Kallosh and M. Shmakova, Generalized Attractor Points in Gauged Supergravity, Phys. Rev. D 84 (2011) 046003 [arXiv:1104.2884] [INSPIRE].
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] [INSPIRE].
K. Hristov, H. Looyestijn and S. Vandoren, BPS black holes in N = 2 D = 4 gauged supergravities, JHEP 08 (2010) 103 [arXiv:1005.3650] [INSPIRE].
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] [INSPIRE].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].
K. Inbasekar and P.K. Tripathy, Stability of Bianchi attractors in Gauged Supergravity, JHEP 10 (2013) 163 [arXiv:1307.1314] [INSPIRE].
K. Inbasekar and P.K. Tripathy, Generalized Attractors in Five-Dimensional Gauged Supergravity, JHEP 09 (2012) 003 [arXiv:1206.3887] [INSPIRE].
D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [INSPIRE].
N. Halmagyi, M. Petrini and A. Zaffaroni, Non-Relativistic Solutions of N = 2 Gauged Supergravity, JHEP 08 (2011) 041 [arXiv:1102.5740] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
H. Lü, C.N. Pope and P.K. Townsend, Domain walls from anti-de Sitter space-time, Phys. Lett. B 391 (1997) 39 [hep-th/9607164] [INSPIRE].
H. Lü, C.N. Pope and J. Rahmfeld, A Construction of Killing spinors on S n, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [INSPIRE].
S.L. Cacciatori, D. Klemm and W.A. Sabra, Supersymmetric domain walls and strings in D = 5 gauged supergravity coupled to vector multiplets, JHEP 03 (2003) 023 [hep-th/0302218] [INSPIRE].
D. Klemm and W.A. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev. D 62 (2000) 024003 [hep-th/0001131] [INSPIRE].
A. Almuhairi and J. Polchinski, Magnetic AdS × R 2 : Supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
A. Ceresole and G. Dall’Agata, General matter coupled N = 2, D = 5 gauged supergravity, Nucl. Phys. B 585 (2000) 143 [hep-th/0004111] [INSPIRE].
M. Günaydin, G. Sierra and P.K. Townsend, Gauging the D = 5 Maxwell-Einstein Supergravity Theories: More on Jordan Algebras, Nucl. Phys. B 253 (1985) 573 [INSPIRE].
M. Gunaydin, G. Sierra, and P. Townsend, The geometry of n = 2 maxwell-einstein supergravity and jordan algebras, Nucl. Phys. B 242 (1984) 244.
M. Günaydin and M. Zagermann, The Gauging of five-dimensional, N = 2 Maxwell-Einstein supergravity theories coupled to tensor multiplets, Nucl. Phys. B 572 (2000) 131 [hep-th/9912027] [INSPIRE].
M. Günaydin and M. Zagermann, The Vacua of 5-D, N = 2 gauged Yang-Mills/Einstein tensor supergravity: Abelian case, Phys. Rev. D 62 (2000) 044028 [hep-th/0002228] [INSPIRE].
B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
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Inbasekar, K., Samanta, R. Stable Bianchi III attractor in U(1) R gauged supergravity. J. High Energ. Phys. 2014, 55 (2014). https://doi.org/10.1007/JHEP08(2014)055
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DOI: https://doi.org/10.1007/JHEP08(2014)055