A non-renormalization theorem for chiral primary 3-point functions

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Article

Abstract

In this note we prove a non-renormalization theorem for the 3-point functions of 1/2 BPS primaries in the four-dimensional \( \mathcal{N} = 4 \) SYM and chiral primaries in two dimensional \( \mathcal{N} = \left( {4,4} \right) \) SCFTs. Our proof is rather elementary: it is based on Ward identities and the structure of the short multiplets of the superconformal algebra and it does not rely on superspace techniques. We also discuss some possible generalizations to less supersymmetric multiplets.

Keywords

Supersymmetric gauge theory Gauge-gravity correspondence AdS-CFT Correspondence 

References

  1. [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] [INSPIRE].
  2. [2]
    S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].MathSciNetADSGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  4. [4]
    S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large-N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].MathSciNetMATHGoogle Scholar
  5. [5]
    E. D’Hoker, D.Z. Freedman and W. Skiba, Field theory tests for correlators in the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 045008 [hep-th/9807098] [INSPIRE].MathSciNetADSGoogle Scholar
  6. [6]
    E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [INSPIRE].
  7. [7]
    M.R. Gaberdiel and I. Kirsch, Worldsheet correlators in AdS 3/CFT 2, JHEP 04 (2007) 050 [hep-th/0703001] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    A. Dabholkar and A. Pakman, Exact chiral ring of AdS 3/CFT 2, Adv. Theor. Math. Phys. 13 (2009) 409 [hep-th/0703022] [INSPIRE].MathSciNetMATHGoogle Scholar
  9. [9]
    A. Pakman and A. Sever, Exact N = 4 correlators of AdS 3/CFT 2, Phys. Lett. B 652 (2007) 60 [arXiv:0704.3040] [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    M. Taylor, Matching of correlators in AdS 3/CFT 2, JHEP 06 (2008) 010 [arXiv:0709.1838] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    K.A. Intriligator, Bonus symmetries of N = 4 super Yang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    K.A. Intriligator and W. Skiba, Bonus symmetry and the operator product expansion of N = 4 Super Yang-Mills, Nucl. Phys. B 559 (1999) 165 [hep-th/9905020] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    B. Eden, P.S. Howe and P.C. West, Nilpotent invariants in N = 4 SYM, Phys. Lett. B 463 (1999) 19 [hep-th/9905085] [INSPIRE].MathSciNetADSGoogle Scholar
  14. [14]
    A. Petkou and K. Skenderis, A nonrenormalization theorem for conformal anomalies, Nucl. Phys. B 561 (1999) 100 [hep-th/9906030] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Explicit construction of nilpotent covariants in N = 4 SYM, Nucl. Phys. B 571 (2000) 71 [hep-th/9910011] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    P. Heslop and P.S. Howe, OPEs and three-point correlators of protected operators in N = 4 SYM, Nucl. Phys. B 626 (2002) 265 [hep-th/0107212] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    A. Basu, M.B. Green and S. Sethi, Some systematics of the coupling constant dependence of N = 4 Yang-Mills, JHEP 09 (2004) 045 [hep-th/0406231] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    J. de Boer, J. Manschot, K. Papadodimas and E. Verlinde, The chiral ring of AdS 3/CFT 2 and the attractor mechanism, JHEP 03 (2009) 030 [arXiv:0809.0507] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    K. Ranganathan, H. Sonoda and B. Zwiebach, Connections on the state space over conformal field theories, Nucl. Phys. B 414 (1994) 405 [hep-th/9304053] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    N. Seiberg, Observations on the moduli space of superconformal field theories, Nucl. Phys. B 303 (1988) 286 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    D. Kutasov, Geometry on the space of conformal field theories and contact terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].MathSciNetADSGoogle Scholar
  23. [23]
    C.A. Cardona and I. Kirsch, Worldsheet four-point functions in AdS 3/CFT 2, JHEP 01 (2011) 015 [arXiv:1007.2720] [INSPIRE]MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    I. Kirsch and T. Wirtz, Worldsheet operator product expansions and p-point functions in AdS 3/CFT 2, JHEP 10 (2011) 049 [arXiv:1106.5876] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].MathSciNetADSGoogle Scholar
  26. [26]
    J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    R. Minasian, G.W. Moore and D. Tsimpis, Calabi-Yau black holes and (0, 4) σ-models, Commun. Math. Phys. 209 (2000) 325 [hep-th/9904217] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  28. [28]
    F. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  29. [29]
    J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  30. [30]
    C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    H. Georgi, Lie algebras in particle physics. From isospin to unified theories, Front. Phys. 54 (1982) 1.MathSciNetGoogle Scholar

Copyright information

© SISSA 2012

Authors and Affiliations

  • Marco Baggio
    • 1
  • Jan de Boer
    • 1
  • Kyriakos Papadodimas
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Theory Group, Physics DepartmentCERNGeneva 23Switzerland

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