Advertisement

Journal of High Energy Physics

, 2010:115 | Cite as

Higher spin gauge theory and holography: the three-point functions

  • Simone Giombi
  • Xi Yin
Article

Abstract

In this paper we calculate the tree level three-point functi ons of Vasiliev’s higher spin gauge theory in AdS 4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the fre e field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.

Keywords

AdS-CFT Correspondence Models of Quantum Gravity 1/N Exp ansion 

References

  1. [1]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].MathSciNetADSzbMATHGoogle Scholar
  2. [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 ].MathSciNetADSGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].MathSciNetzbMATHGoogle Scholar
  4. [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 ].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    B. Sundborg, Stringy gravity, interacting tensionless strings and mass less higher spins, Nucl. Phys. (Proc. Suppl.) 102 (2001) 113 [hep-th/0103247] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    P. Haggi-Mani and B. Sundborg, Free large-N supersymmetric Yang-Mills theory as a string theory, JHEP 04 (2000) 031 [hep-th/0002189] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [SPIRES].MathSciNetzbMATHGoogle Scholar
  8. [8]
    N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, On the spectrum of AdS/CFT beyond supergravity, JHEP 02 (2004) 001 [hep-th/0310292] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, Higher spin symmetry and N = 4 SYM, JHEP 07 (2004) 058 [hep-th/0405057] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [SPIRES]. MathSciNetADSGoogle Scholar
  11. [11]
    R. Gopakumar, From free fields to AdS. II, Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [SPIRES].MathSciNetADSGoogle Scholar
  12. [12]
    R. Gopakumar, From free fields to AdS. III, Phys. Rev. D 72 (2005) 066008 [hep-th/0504229] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    J.R. David and R. Gopakumar, From spacetime to worldsheet: four point correlators, JHEP 01 (2007) 063 [hep-th/0606078] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    N. Berkovits, Perturbative super-Yang-Mills from the topological AdS 5 × S 5 σ-model, JHEP 09 (2008) 088 [arXiv:0806.1960] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    N. Berkovits, Simplifying and extending the AdS 5 × S 5 pure spinor formalism, JHEP 09 (2009) 051 [arXiv:0812.5074] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    J. Isberg, U. Lindström and B. Sundborg, Space-time symmetries of quantized tensionless strings, Phys. Lett. B 293 (1992) 321 [hep-th/9207005] [SPIRES].ADSGoogle Scholar
  17. [17]
    J. Isberg, U. Lindström, B. Sundborg and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys. B 411 (1994) 122 [hep-th/9307108] [SPIRES].ADSCrossRefGoogle Scholar
  18. [18]
    U. Lindström and M. Zabzine, Tensionless strings, WZW models at critical level and massless higher spin fields, Phys. Lett. B 584 (2004) 178 [hep-th/0305098] [SPIRES].ADSGoogle Scholar
  19. [19]
    G. Bonelli, On the covariant quantization of tensionless bosonic strin gs in AdS spacetime, JHEP 11 (2003) 028 [hep-th/0309222] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    I. Bakas and C. Sourdis, On the tensionless limit of gauged WZW models, JHEP 06 (2004) 049 [hep-th/0403165] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    A. Sagnotti and M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B 682 (2004) 83 [hep-th/0311257] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [SPIRES].MathSciNetADSGoogle Scholar
  23. [23]
    S.E. Konstein, M.A. Vasiliev and V.N. Zaikin, Conformal higher spin currents in any dimension and AdS/CFT correspondence, JHEP 12 (2000) 018 [hep-th/0010239] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. [24]
    O.V. Shaynkman and M.A. Vasiliev, Higher spin conformal symmetry for matter fields in 2+1 dimensions, Theor. Math. Phys. 128 (2001) 1155 [Teor. Mat. Fiz. 128 (2001) 378] [hep-th/0103208] [SPIRES].zbMATHCrossRefGoogle Scholar
  25. [25]
    E. Sezgin and P. Sundell, Doubletons and 5D higher spin gauge theory, JHEP 09 (2001) 036 [hep-th/0105001] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    M.A. Vasiliev, Conformal higher spin symmetries of 4D massless supermultiplets and osp(L, 2M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [SPIRES].MathSciNetADSGoogle Scholar
  27. [27]
    A. Mikhailov, Notes on higher spin symmetries, hep-th/0201019 [SPIRES].
  28. [28]
    E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. B 660 (2003) 403] [hep-th/0205131] [SPIRES]. MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    S.S. Gubser and I.R. Klebanov, A universal result on central charges in the presence of double-trace deformations, Nucl. Phys. B 656 (2003) 23 [hep-th/0212138] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    M.A. Vasiliev, Higher-spin gauge theories in four, three and two dimension s, Int. J. Mod. Phys. D5 (1996) 763 [hep-th/9611024] [SPIRES].MathSciNetADSGoogle Scholar
  32. [32]
    M.A. Vasiliev, Higher spin gauge theories: star-product and AdS space, hep-th/9910096 [SPIRES].
  33. [33]
    M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS d, Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [SPIRES].MathSciNetADSGoogle Scholar
  34. [34]
    X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [SPIRES].
  35. [35]
    E. Sezgin and P. Sundell, Analysis of higher spin field equations in four dimensions, JHEP 07 (2002) 055 [hep-th/0205132] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [SPIRES].MathSciNetADSzbMATHCrossRefGoogle Scholar
  37. [37]
    A.C. Petkou, Evaluating the AdS dual of the critical O(N) vector model, JHEP 03 (2003) 049 [hep-th/0302063] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    R.G. Leigh and A.C. Petkou, Holography of the N = 1 higher-spin theory on AdS 4, JHEP 06 (2003) 011 [hep-th/0304217] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    A. Fotopoulos and M. Tsulaia, Gauge invariant Lagrangians for free and interacting higher spin fields. A review of the BRST formulation, Int. J. Mod. Phys. A 24 (2009) 1 [arXiv:0805.1346] [SPIRES].MathSciNetADSGoogle Scholar
  41. [41]
    E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [SPIRES].
  42. [42]
    D.E. Diaz and H. Dorn, On the AdS higher spin/O(N) vector model correspondence: degeneracy of the holographic image, JHEP 07 (2006) 022 [hep-th/0603084] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    L. Girardello, M. Porratiand A. Zaffaroni, 3D interacting CFTs and generalized Higgs phenomenon in higher spin theories on AdS, Phys. Lett. B 561 (2003) 289 [hep-th/0212181] [SPIRES].MathSciNetADSGoogle Scholar
  44. [44]
    S.S. Gubser and I. Mitra, Double-trace operators and one-loop vacuum energy in AdS/C FT, Phys. Rev. D 67 (2003) 064018 [hep-th/0210093] [SPIRES].MathSciNetADSGoogle Scholar
  45. [45]
    E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [SPIRES]. MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    K. Lang and W. Rühl, Anomalous dimensions of tensor fields of arbitrary rank for critical nonlinear O(N) σ-models at 2 <d < 4 to first order in 1/N, Z. Phys. C 51 (1991) 127 [SPIRES]. Google Scholar
  47. [47]
    K. Lang and W. Rühl, Field algebra for critical O(N) vector nonlinear σ-models at 2 < d < 4, Z. Phys. C 50 (1991) 285 [SPIRES].Google Scholar
  48. [48]
    K. Lang and W. Rühl, The critical O(N) σ-model at dimension 2 < d < 4 and order 1/N 2 : operator product expansions and renormalization, Nucl. Phys. B 377 (1992) 371 [SPIRES].ADSCrossRefGoogle Scholar
  49. [49]
    K. Lang and W. Rühl, The scalar ancestor of the energy momentum field in critical σ-models at 2 < d < 4, Phys. Lett. B 275 (1992) 93 [SPIRES].ADSGoogle Scholar
  50. [50]
    K. Lang and W. Rühl, The critical O(N) σ-model at dimensions 2 < d < 4: fusion coefficients and anomalous dimensions, Nucl. Phys. B 400 (1993) 597 [SPIRES].ADSCrossRefGoogle Scholar
  51. [51]
    D.I. Kazakov, Calculation of Feynman integrals by the method of ‘uniquene ss’, Theor. Math. Phys. 58 (1984) 223 [Teor. Mat. Fiz. 58 (1984) 343] [SPIRES].MathSciNetCrossRefGoogle Scholar
  52. [52]
    D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [SPIRES].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Center for the Fundamental Laws of Nature, Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.

Personalised recommendations