Skip to main content
Springer Nature Link
Log in

Fermions and D = 11 supergravity on squashed Sasaki-Einstein manifolds

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of D = 11 supergravity compactified on squashed seven-dimensional Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have (2 + 1)-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which most notably include charged scalar and form fields. We demonstrate that our results are consistent with the expected supersymmetric structure of the lower dimensional theory, and apply them to a specific example which is relevant to the study of (2 + 1)-dimensional holographic superconductors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.M. Maldacena, The large-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].

    Article  MathSciNet  MATH  Google Scholar 

  2. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MathSciNet  MATH  Google Scholar 

  4. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χSB-resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. J.M. Maldacena and C. Núñez, Towards the large-N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].

    ADS  Google Scholar 

  8. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].

    Article  ADS  Google Scholar 

  9. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  11. K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. 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].

    Article  MathSciNet  ADS  Google Scholar 

  13. C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [SPIRES].

    Article  ADS  Google Scholar 

  15. H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 11d supergravity on AdS 7 × S 4 and self-duality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [SPIRES].

    ADS  Google Scholar 

  16. 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].

    Article  ADS  Google Scholar 

  17. P.G.O. Freund and M.A. Rubin, Dynamics of Dimensional Reduction, Phys. Lett. B 97 (1980) 233 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  18. 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].

    MathSciNet  ADS  Google Scholar 

  19. 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].

    Article  ADS  Google Scholar 

  20. 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].

    Article  MathSciNet  ADS  Google Scholar 

  21. 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].

    Article  MathSciNet  ADS  Google Scholar 

  22. 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].

    Article  ADS  Google Scholar 

  23. J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. 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].

    Article  MathSciNet  ADS  Google Scholar 

  26. 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].

    Article  MathSciNet  ADS  Google Scholar 

  27. J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to N = 4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. 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].

    ADS  Google Scholar 

  29. 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].

    Article  MathSciNet  ADS  Google Scholar 

  30. 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].

    Article  MathSciNet  ADS  Google Scholar 

  31. C.N. Pope and K.S. Stelle, Zilch Currents, Supersymmetry And Kaluza-Klein Consistency, Phys. Lett. B 198 (1987) 151 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  32. M. Cvetič, H. Lü and C.N. Pope, Consistent Kaluza-Klein sphere reductions, Phys. Rev. D 62 (2000) 064028 [hep-th/0003286] [SPIRES].

    ADS  Google Scholar 

  33. T. Faulkner, G.T. Horowitz, J. McGreevy, M.M. Roberts and D. Vegh, Photoemission ’experiments’ on holographic superconductors, JHEP 03 (2010) 121 [arXiv:0911.3402] [SPIRES].

    Article  ADS  Google Scholar 

  34. S.S. Gubser, F.D. Rocha and P. Talavera, Normalizable fermion modes in a holographic superconductor, JHEP 10 (2010) 087 [arXiv:0911.3632] [SPIRES].

    Article  ADS  Google Scholar 

  35. M. Ammon, J. Erdmenger, M. Kaminski and A. O’Bannon, Fermionic Operator Mixing in Holographic p-wave Superfluids, JHEP 05 (2010) 053 [arXiv:1003.1134] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. M.J. Duff, B.E.W. Nilsson and C.N. Pope, The Criterion For Vacuum Stability In Kaluza-Klein Supergravity, Phys. Lett. B 139 (1984) 154 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  38. D. Martelli, J. Sparks and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys. 280 (2008) 611 [hep-th/0603021] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. N. Hitchin, Harmonic spinors, Adv. Math. 14 (1974) 1.

    Article  MathSciNet  MATH  Google Scholar 

  40. C.N. Pope and N.P. Warner, Two new classes of compactifications of d = 11 supergravity, Class. Quant. Grav. 2 (1985) L1 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. G.W. Gibbons, S.A. Hartnoll and C.N. Pope, Bohm and Einstein-Sasaki metrics, black holes and cosmological event horizons, Phys. Rev. D 67 (2003) 084024 [hep-th/0208031] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  42. H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, arXiv:0903.2477 [SPIRES].

  43. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS2, arXiv:0907.2694 [SPIRES].

  44. J.-W. Chen, Y.-J. Kao and W.-Y. Wen, Peak-Dip-Hump from Holographic Superconductivity, Phys. Rev. D 82 (2010) 026007 [arXiv:0911.2821] [SPIRES].

    ADS  Google Scholar 

  45. S.S. Gubser, F.D. Rocha and A. Yarom, Fermion correlators in non-abelian holographic superconductors, JHEP 11 (2010) 085 [arXiv:1002.4416] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. D.Z. Freedman and A.K. Das, Gauge Internal Symmetry in Extended Supergravity, Nucl. Phys. B 120 (1977) 221 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. E.S. Fradkin and M.A. Vasiliev, Model of Supergravity with Minimal Electromagnetic Interaction, Lebedev Institute preprint, LEBEDEV-76-197 [SPIRES].

  48. L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Michigan Center for Theoretical Physics, Randall Laboratory of Physics, University of Michigan, Ann Arbor, MI, 48109, U.S.A.

    Ibrahima Bah, Alberto Faraggi & Leopoldo A. Pando Zayas

  2. Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, IL, 61801, U.S.A.

    Juan I. Jottar & Robert G. Leigh

Authors
  1. Ibrahima Bah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alberto Faraggi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan I. Jottar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Robert G. Leigh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Leopoldo A. Pando Zayas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan I. Jottar.

Additional information

ArXiv ePrint: 1008.1423

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bah, I., Faraggi, A., Jottar, J.I. et al. Fermions and D = 11 supergravity on squashed Sasaki-Einstein manifolds. J. High Energ. Phys. 2011, 68 (2011). https://doi.org/10.1007/JHEP02(2011)068

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2011)068

Keywords

Search

Navigation