Advertisement

SUSY properties of warped AdS3

  • Jaehoon Jeong
  • Eoin Ó ColgáinEmail author
  • Kentaroh Yoshida
Open Access
Article

Abstract

We examine supersymmetric properties of null-warped AdS3, or alternatively Schrödinger geometries, dual to putative warped CFTs in two dimensions. We classify super Schrödinger subalgebras of the superalgebra psu(1, 1|2) ⊕ psu(1, 1|2), corresponding to the superconformal algebra of the AdS3 × S3 geometry. We comment on geometric realisations and provide a string theory description with enhanced supersymmetry in terms of intersecting D3-branes. For type IIB supergravity solutions based on T 1,1, we consider the relationship between five-dimensional Schrödinger solutions and their three-dimensional null-warped counterparts, corresponding to R symmetry twists. Finally, we study a family of null-warped AdS3 solutions in a setting where there is an ambiguity over the R symmetry and confirm that, for examples admitting a Kaluza-Klein (KK) reduction to three dimensions, the minimisation of a real superpotential of the three-dimensional gauged supergravity captures the central charge and R symmetry.

Keywords

AdS-CFT Correspondence Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].ADSMathSciNetGoogle Scholar
  6. [6]
    D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 black holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    B.E.W. Nilsson, Critical solutions in topologically gauged N = 8 CFTs in three dimensions, arXiv:1304.2270 [INSPIRE].
  8. [8]
    N.S. Deger, A. Kaya, H. Samtleben and E. Sezgin, Supersymmetric warped AdS in extended topologically massive supergravity, arXiv:1311.4583 [INSPIRE].
  9. [9]
    M. Gary, D. Grumiller and R. Rashkov, Towards non-AdS holography in 3-dimensional higher spin gravity, JHEP 03 (2012) 022 [arXiv:1201.0013] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    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] [INSPIRE].ADSMathSciNetGoogle Scholar
  12. [12]
    K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    S. Detournay and M. Guica, Stringy Schrödinger truncations, JHEP 08 (2013) 121 [arXiv:1212.6792] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    P. Karndumri and E. Ó Colgáin, 3D supergravity from wrapped D3-branes, JHEP 10 (2013) 094 [arXiv:1307.2086] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  16. [16]
    M. Guica, A Fefferman-Graham-like expansion for null warped AdS 3, arXiv:1111.6978 [INSPIRE].
  17. [17]
    M. Guica, Decrypting the warped black strings, JHEP 11 (2013) 025 [arXiv:1305.7249] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    J. Hartong and B. Rollier, Particle number and 3D Schrödinger holography, arXiv:1305.3653 [INSPIRE].
  19. [19]
    S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].ADSGoogle Scholar
  20. [20]
    S. El-Showk and M. Guica, Kerr/CFT, dipole theories and nonrelativistic CFTs, JHEP 12 (2012) 009 [arXiv:1108.6091] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    W. Song and A. Strominger, Warped AdS 3 /dipole-CFT duality, JHEP 05 (2012) 120 [arXiv:1109.0544] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    C. Duval and P.A. Horváthy, On Schrödinger superalgebras, J. Math. Phys. 35 (1994) 2516 [hep-th/0508079] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  23. [23]
    M. Sakaguchi and K. Yoshida, Super Schrödinger algebra in AdS/CFT, J. Math. Phys. 49 (2008) 102302 [arXiv:0805.2661] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    M. Sakaguchi and K. Yoshida, More super Schrödinger algebras from psu(2, 2|4), JHEP 08 (2008) 049 [arXiv:0806.3612] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    M. Sakaguchi and K. Yoshida, Supersymmetric extensions of non-relativistic scaling algebras, Symmetry 4 (2012) 517 [INSPIRE].CrossRefMathSciNetGoogle Scholar
  26. [26]
    M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    V.K. Dobrev, Non-relativistic holographya group-theoretical perspective, Int. J. Mod. Phys. A 29 (2014) 1430001 [arXiv:1312.0219] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    Y. Nakayama, M. Sakaguchi and K. Yoshida, Non-relativistic M2-brane gauge theory and new superconformal algebra, JHEP 04 (2009) 096 [arXiv:0902.2204] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    K.-M. Lee, S. Lee and S. Lee, Nonrelativistic superconformal M2-brane theory, JHEP 09 (2009) 030 [arXiv:0902.3857] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    E. Ó Colgáin and H. Yavartanoo, NR CFT 3 duals in M-theory, JHEP 09 (2009) 002 [arXiv:0904.0588] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    H. Ooguri and C.-S. Park, Supersymmetric non-relativistic geometries in M-theory, Nucl. Phys. B 824 (2010) 136 [arXiv:0905.1954] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    J. Jeong, H.-C. Kim, S. Lee, E. Ó Colgáin and H. Yavartanoo, Schrödinger invariant solutions of M-theory with enhanced supersymmetry, JHEP 03 (2010) 034 [arXiv:0911.5281] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    A. Donos and J.P. Gauntlett, Schrödinger invariant solutions of type IIB with enhanced supersymmetry, JHEP 10 (2009) 073 [arXiv:0907.1761] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    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].ADSCrossRefGoogle Scholar
  35. [35]
    I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  36. [36]
    I. Bena, M. Guica and W. Song, Un-twisting the NHEK with spectral flows, JHEP 03 (2013) 028 [arXiv:1203.4227] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  37. [37]
    T. Azeyanagi, D.M. Hofman, W. Song and A. Strominger, The spectrum of strings on warped AdS 3 × S3, JHEP 04 (2013) 078 [arXiv:1207.5050] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  38. [38]
    N. Kim, AdS 3 solutions of IIB supergravity from D3-branes, JHEP 01 (2006) 094 [hep-th/0511029] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    N. Bobev, A. Kundu and K. Pilch, Supersymmetric IIB solutions with Schrödinger symmetry, JHEP 07 (2009) 107 [arXiv:0905.0673] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  42. [42]
    P. Karndumri and E. Ó Colgáin, Supergravity dual of c-extremization, Phys. Rev. D 87 (2013) 101902 [arXiv:1302.6532] [INSPIRE].ADSGoogle Scholar
  43. [43]
    Y. Kosmann, A note on Lie-Lorentz derivatives, Ann. Mat. Pur. Appl. 91 (1972) 317.CrossRefzbMATHMathSciNetGoogle Scholar
  44. [44]
    J.M. Figueroa-O’Farrill, On the supersymmetries of anti-de Sitter vacua, Class. Quant. Grav. 16 (1999) 2043 [hep-th/9902066] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  45. [45]
    Y. Nakayama, S. Ryu, M. Sakaguchi and K. Yoshida, A family of super Schrödinger invariant Chern-Simons matter systems, JHEP 01 (2009) 006 [arXiv:0811.2461] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  46. [46]
    Y. Nakayama, M. Sakaguchi and K. Yoshida, Interacting SUSY-singlet matter in non-relativistic Chern-Simons theory, J. Phys. A 42 (2009) 195402 [arXiv:0812.1564] [INSPIRE].ADSMathSciNetGoogle Scholar
  47. [47]
    J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [INSPIRE].ADSMathSciNetGoogle Scholar
  48. [48]
    P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    S.S. Pufu, I.R. Klebanov, T. Klose and J. Lin, Greens functions and non-singlet glueballs on deformed conifolds, J. Phys. A 44 (2011) 055404 [arXiv:1009.2763] [INSPIRE].ADSMathSciNetGoogle Scholar
  50. [50]
    N. Bobev and B.C. van Rees, Schrödinger deformations of AdS 3 × S 3, JHEP 08 (2011) 062 [arXiv:1102.2877] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    P. Kraus and E. Perlmutter, Universality and exactness of Schrödinger geometries in string and M-theory, JHEP 05 (2011) 045 [arXiv:1102.1727] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  52. [52]
    M. Naka, Various wrapped branes from gauged supergravities, hep-th/0206141 [INSPIRE].
  53. [53]
    J.P. Gauntlett, N. Kim and D. Waldram, Supersymmetric AdS 3 , AdS 2 and bubble solutions, JHEP 04 (2007) 005 [hep-th/0612253] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  54. [54]
    C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  55. [55]
    J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  56. [56]
    A. Adams, K. Balasubramanian and J. McGreevy, Hot spacetimes for cold atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    S.A. Hartnoll and K. Yoshida, Families of IIB duals for nonrelativistic CFTs, JHEP 12 (2008) 071 [arXiv:0810.0298] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  58. [58]
    A. Donos and J.P. Gauntlett, Supersymmetric solutions for non-relativistic holography, JHEP 03 (2009) 138 [arXiv:0901.0818] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  59. [59]
    N. Bobev and A. Kundu, Deformations of holographic duals to non-relativistic CFTs, JHEP 07 (2009) 098 [arXiv:0904.2873] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  60. [60]
    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] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  61. [61]
    E. Ó Colgáin, O. Varela and H. Yavartanoo, Non-relativistic M-theory solutions based on Kähler-Einstein spaces, JHEP 07 (2009) 081 [arXiv:0906.0261] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    G. Itsios, Y. Lozano, E. Ó Colgáin and K. Sfetsos, Non-Abelian T-duality and consistent truncations in type-II supergravity, JHEP 08 (2012) 132 [arXiv:1205.2274] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    D. Mallayev, J.F. Vazquez-Poritz and Z. Zhang, Marginal deformations of non-relativistic field theories, arXiv:1309.3257 [INSPIRE].
  64. [64]
    T. Ortín, SL(2, \( \mathbb{R} \)) duality covariance of Killing spinors in axion-dilaton black holes, Phys. Rev. D 51 (1995) 790 [hep-th/9404035] [INSPIRE].ADSGoogle Scholar
  65. [65]
    A. Bergman and O.J. Ganor, Dipoles, twists and noncommutative gauge theory, JHEP 10 (2000) 018 [hep-th/0008030] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  66. [66]
    A. Bergman, K. Dasgupta, O.J. Ganor, J.L. Karczmarek and G. Rajesh, Nonlocal field theories and their gravity duals, Phys. Rev. D 65 (2002) 066005 [hep-th/0103090] [INSPIRE].ADSMathSciNetGoogle Scholar
  67. [67]
    K. Dasgupta and M.M. Sheikh-Jabbari, Noncommutative dipole field theories, JHEP 02 (2002) 002 [hep-th/0112064] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  68. [68]
    B.E.W. Nilsson and C.N. Pope, Hopf fibration of eleven-dimensional supergravity, Class. Quant. Grav. 1 (1984) 499 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  69. [69]
    K.A. Intriligator and B. Wecht, The exact superconformal R-symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  70. [70]
    E. Ó Colgáin, Self-duality of the D1-D5 near-horizon, JHEP 04 (2012) 047 [arXiv:1202.3416] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    I. Adam, A. Dekel and Y. Oz, On integrable backgrounds self-dual under fermionic T-duality, JHEP 04 (2009) 120 [arXiv:0902.3805] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  72. [72]
    S. Cucu, H. Lü and J.F. Vazquez-Poritz, Interpolating from AdS D−2 × S 2 to AdS D , Nucl. Phys. B 677 (2004) 181 [hep-th/0304022] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    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] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  77. [77]
    M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    P. Dey and S. Roy, Intersecting D-branes and Lifshitz-like space-time, Phys. Rev. D 86 (2012) 066009 [arXiv:1204.4858] [INSPIRE].ADSGoogle Scholar
  80. [80]
    I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  81. [81]
    E. Ó Colgáin and H. Samtleben, 3D gauged supergravity from wrapped M5-branes with AdS/CMT applications, JHEP 02 (2011) 031 [arXiv:1012.2145] [INSPIRE].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Jaehoon Jeong
    • 1
  • Eoin Ó Colgáin
    • 2
    • 3
    • 4
    Email author
  • Kentaroh Yoshida
    • 5
  1. 1.Department of Physics, College of ScienceYonsei UniversitySeoulKorea
  2. 2.C.N. Yang Institute for Theoretical PhysicsSUNY Stony BrookStony BrookU.S.A.
  3. 3.Department of MathematicsUniversity of SurreyGuildfordU.K.
  4. 4.Departamento de FísicaUniversidad de OviedoOviedoSpain
  5. 5.Department of PhysicsKyoto UniversityKyotoJapan

Personalised recommendations