Skip to main content
SpringerLink
Log in

Strings on bubbling geometries

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

Abstract

We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wave-function.

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

Access this article

Log in via an institution

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. 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 

  2. E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, hep-th/0201253 [SPIRES].

  3. G.T. Horowitz and J. Polchinski, Gauge/gravity duality, gr-qc/0602037 [SPIRES].

  4. S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [SPIRES].

    MathSciNet  Google Scholar 

  5. D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. S.E. Vazquez, Reconstructing 1/2 BPS space-time metrics from matrix models and spin chains, Phys. Rev. D 75 (2007) 125012 [hep-th/0612014] [SPIRES].

    ADS  Google Scholar 

  8. H.-Y. Chen, D.H. Correa and G.A. Silva, Geometry and topology of bubble solutions from gauge theory, Phys. Rev. D 76 (2007) 026003 [hep-th/0703068] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. R.d.M. Koch, Geometries from Young diagrams, JHEP 11 (2008) 061 [arXiv:0806.0685] [SPIRES].

    Article  Google Scholar 

  10. R.d.M. Koch, N. Ives and M. Stephanou, Correlators in nontrivial backgrounds, Phys. Rev. D 79 (2009) 026004 [arXiv:0810.4041] [SPIRES].

    ADS  Google Scholar 

  11. R. de Mello Koch, T.K. Dey, N. Ives and M. Stephanou, Correlators of operators with a large R-charge, JHEP 08 (2009) 083 [arXiv:0905.2273] [SPIRES].

    Article  Google Scholar 

  12. R.d.M. Koch and J. Murugan, Emergent spacetime, arXiv:0911.4817 [SPIRES].

  13. G. Mandal, Fermions from half-BPS supergravity, JHEP 08 (2005) 052 [hep-th/0502104] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. L. Grant, L. Maoz, J. Marsano, K. Papadodimas and V.S. Rychkov, Minisuperspace quantization of ’bubbling AdS’ and free fermion droplets, JHEP 08 (2005) 025 [hep-th/0505079] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. P. Hořava and P.G. Shepard, Topology changing transitions in bubbling geometries, JHEP 02 (2005) 063 [hep-th/0502127] [SPIRES].

    ADS  Google Scholar 

  16. T.W. Brown, R. de Mello Koch, S. Ramgoolam and N. Toumbas, Correlators, probabilities and topologies in N = 4 SYM, JHEP 03 (2007) 072 [hep-th/0611290] [SPIRES].

    Article  ADS  Google Scholar 

  17. S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [SPIRES].

    Article  ADS  Google Scholar 

  18. O. Lunin, On gravitational description of Wilson lines, JHEP 06 (2006) 026 [hep-th/0604133] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. E. D’Hoker, J. Estes and M. Gutperle, Gravity duals of half-BPS Wilson loops, JHEP 06 (2007) 063 [arXiv:0705.1004] [SPIRES].

    Article  MathSciNet  Google Scholar 

  21. S. Gukov and E. Witten, Rigid surface operators, arXiv:0804.1561 [SPIRES].

  22. J. Gomis and S. Matsuura, Bubbling surface operators and S-duality, JHEP 06 (2007) 025 [arXiv:0704.1657] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. H. Lin and J.M. Maldacena, Fivebranes from gauge theory, Phys. Rev. D 74 (2006) 084014 [hep-th/0509235] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  24. J. Gomis and C. Romelsberger, Bubbling defect CFT’s, JHEP 08 (2006) 050 [hep-th/0604155] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. D. Berenstein, Large-N BPS states and emergent quantum gravity, JHEP 01 (2006) 125 [hep-th/0507203] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. D. Berenstein and R. Cotta, A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects, JHEP 04 (2007) 071 [hep-th/0702090] [SPIRES].

    Article  ADS  Google Scholar 

  27. B. Chen et al., Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity, JHEP 10 (2007) 003 [arXiv:0704.2233] [SPIRES].

    Article  ADS  Google Scholar 

  28. E. Gava, G. Milanesi, K.S. Narain and M. O’Loughlin, 1/8 BPS states in AdS/CFT, JHEP 05 (2007) 030 [hep-th/0611065] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. A. Donos, BPS states in type IIB SUGRA with SO(4) × SO(2) (gauged) symmetry, JHEP 05 (2007) 072 [hep-th/0610259] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. N. Kim, AdS 3 solutions of IIB supergravity from D3-branes, JHEP 01 (2006) 094 [hep-th/0511029] [SPIRES].

    Article  ADS  Google Scholar 

  31. O. Lunin, Brane webs and 1/4-BPS geometries, JHEP 09 (2008) 028 [arXiv:0802.0735] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. T.W. Brown, P.J. Heslop and S. Ramgoolam, Diagonal multi-matrix correlators and BPS operators in N = 4 SYM, JHEP 02 (2008) 030 [arXiv:0711.0176] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. Y. Kimura and S. Ramgoolam, Branes, anti-branes and brauer algebras in gauge-gravity duality, JHEP 11 (2007) 078 [arXiv:0709.2158] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. R. Bhattacharyya, S. Collins and R.d.M. Koch, Exact multi-matrix correlators, JHEP 03 (2008) 044 [arXiv:0801.2061] [SPIRES].

    Article  ADS  Google Scholar 

  35. D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. R. Roiban, A. Tirziu and A.A. Tseytlin, Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz type effective 2 − D actions, J. Phys. A 39 (2006) 13129 [hep-th/0604199] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  37. S.S. Gubser and J.J. Heckman, Thermodynamics of R-charged black holes in AdS 5 from effective strings, JHEP 11 (2004) 052 [hep-th/0411001] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. M.M. Caldarelli, D. Klemm and P.J. Silva, Chronology protection in Anti-de Sitter, Class. Quant. Grav. 22 (2005) 3461 [hep-th/0411203] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  39. V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The library of Babel: on the origin of gravitational thermodynamics, JHEP 12 (2005) 006 [hep-th/0508023] [SPIRES].

    ADS  Google Scholar 

  40. L. D’Errico, W. Mueck and R. Pettorino, Stretched horizon and entropy of superstars, JHEP 05 (2007) 063 [hep-th/0703223] [SPIRES].

    Article  Google Scholar 

  41. V. Balasubramanian, B. Czech, K. Larjo, D. Marolf and J. Simon, Quantum geometry and gravitational entropy, JHEP 12 (2007) 067 [arXiv:0705.4431] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. N.V. Suryanarayana, Half-BPS giants, free fermions and microstates of superstars, JHEP 01 (2006) 082 [hep-th/0411145] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. H.-H. Shieh, G. van Anders and M. Van Raamsdonk, Coarse-graining the Lin-Maldacena geometries, JHEP 09 (2007) 059 [arXiv:0705.4308] [SPIRES].

    Article  ADS  Google Scholar 

  44. W.-M. Zhang, D.H. Feng and R. Gilmore, Coherent states: theory and some applications, Rev. Mod. Phys. 62 (1990) 867 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. J.R. Klauder and B.S. Skagerstam, Coherent states, World Scientific, Singapore (1985).

    MATH  Google Scholar 

  46. A. Perelomov, Generalized coherent states and their applications, Springer-Verlag, Berlin Germay (1986).

    MATH  Google Scholar 

  47. D.M. Hofman and J.M. Maldacena, Giant magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [SPIRES].

    MathSciNet  Google Scholar 

  48. N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [SPIRES].

    MathSciNet  Google Scholar 

  49. N. Beisert, The analytic Bethe ansatz for a chain with centrally extended SU(2|2) symmetry, J. Stat. Mech. (2007) P01017 [nlin/0610017].

  50. V.G. Filev and C.V. Johnson, Operators with large quantum numbers, spinning strings and giant gravitons, Phys. Rev. D 71 (2005) 106007 [hep-th/0411023] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  51. H. Ebrahim and A.E. Mosaffa, Semiclassical string solutions on 1/2 BPS geometries, JHEP 01 (2005) 050 [hep-th/0501072] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  52. M. Alishahiha, H. Ebrahim, B. Safarzadeh and M.M. Sheikh-Jabbari, Semi-classical probe strings on giant gravitons backgrounds, JHEP 11 (2005) 005 [hep-th/0509160] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Particle Physics, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Hai Lin, Alexander Morisse & Jonathan P. Shock

Authors
  1. Hai Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Morisse
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jonathan P. Shock
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonathan P. Shock.

Additional information

ArXiv ePrint: 1003.4190

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, H., Morisse, A. & Shock, J.P. Strings on bubbling geometries. J. High Energ. Phys. 2010, 55 (2010). https://doi.org/10.1007/JHEP06(2010)055

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2010)055

Keywords

Search

Navigation