Letters in Mathematical Physics

, Volume 62, Issue 2, pp 171–184 | Cite as

A Comment on the Dual Field in the AdS–CFT Correspondence

  • M. Dütsch
  • K.-H. Rehren


In the perturbative AdS–CFT correspondence, the dual field whose source are the prescribed boundary values of a bulk field in the functional integral, and the boundary limit of the quantized bulk field are the same thing. This statement is due to the fact that Witten graphs are boundary limits of the corresponding Feynman graphs for the bulk fields, and hence the dual conformal correlation functions are limits of bulk correlation functions. This manifestation of duality is analyzed in terms of the underlying functional integrals of different structure.

anti-de Sitter conformal field theory 


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  1. 1.
    Banks, T., Douglas, M. R., Horowitz, G. T. and Martinec, E. J.: AdS dynamics from conformal field theory, hep-th/9808016.Google Scholar
  2. 2.
    Bertola, M., Bros, J., Moschella, U. and Schaeffer, R.: A general construction of conformal field theories from scalar anti-de Sitter quantum field theories, Nuclear Phys. B 587 (2000), 619-644 [=hep-th/9908140].Google Scholar
  3. 3.
    Breitenlohner, P. and Freedman, D. Z.: Stability in gauged extended supergravity, Ann. Phys. (N.Y.) 144 (1982), 249-281.Google Scholar
  4. 4.
    Brunetti, R. and Fredenhagen, K.: Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds, Comm. Math. Phys. 208 (2000), 623-661.Google Scholar
  5. 5.
    Borchers, H.-J.: Field operators as C functions in spacelike directions, Nuovo Cimento 33 (1964), 1600-1613.Google Scholar
  6. 6.
    Dütsch, M. and Rehren, K.-H.: Generalized free fields and the AdS-CFT correspondence, math-ph/0209035.Google Scholar
  7. 7.
    Freedman, D. Z., Mathur, S. D., Matusis, A. and Rastelli, L.: Correlation functions in the CFTd/AdSd+1 correspondence, Nuclear Phys. B 546 (1999), 96-118; Comments on 4-point functions in the CFT/AdS correspondence, Phys. Lett. B 452 (1999), 61-68.Google Scholar
  8. 8.
    Gubser, S. S., Klebanov, I. R. and Polyakov, A. M.: Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998), 105-114.Google Scholar
  9. 9.
    Haag, R.: On quantum field theories, Dan. Mat. Fys. Medd. 29(12) (1955) reprinted in: L. Klein (ed.), Dispersion Relations and the Abstract Approach to Field Theory, Gordon & Breach, New York, 1961; Local Quantum Physics, Springer, New York, 1992 (Chap. II.1.1).Google Scholar
  10. 10.
    Hoffmann, L., Petkou, A. C. and Rühl, W.: A note on the analyticity of AdS scalar exchange graphs in the crossed channel, Phys. Lett. B 478 (2000), 320-326; Aspects of the conformal operator product expansion in AdS/CFT correspondence, Adv. Theor. Math. Phys. 4 (2000), no. 3 [hep-th/0002154].Google Scholar
  11. 11.
    Jost, R.: The General Theory of Quantized Fields, Amer. Math. Soc., Providence, RI, 1965.Google Scholar
  12. 12.
    Klebanov, I. R. and Witten, E.: AdS/CFT correspondence and symmetry breaking, Nuclear Phys. B 556 (1999), 89-114.Google Scholar
  13. 13.
    Maldacena, J. M.: The large N limit of superconformal field theories and supergravity, Adv. Theoret. Math. Phys. 2 (1998), 231-252.Google Scholar
  14. 14.
    Kniemeyer, O.: Untersuchungen am erzeugenden Funktional der AdS-CFT-Korrespondenz, diploma thesis, Go¨ ttingen, 2002.Google Scholar
  15. 15.
    Licht, A. L.: A generalized asymptotic condition, Ann. Phys. (N.Y.) 34 (1965), 161-186.Google Scholar
  16. 16.
    Osterwalder, K. and Schrader, R.: Axioms for Euclidean Green's functions, 1+2, Comm. Math. Phys. 31 (1973) 83-112, and ibid. 42 (1975) 281-305.Google Scholar
  17. 17.
    Rehren, K.-H.: Algebraic holography, Ann. H. Poincaré 1 (2000), 607-623; Local quantum observables in the AdS-CFT correspondence, Phys. Lett. B 493 (2000), 383-388.Google Scholar
  18. 18.
    Schroer, B.: Lightfront formalism versus holography and chiral scanning, hep-th/0108203.Google Scholar
  19. 19.
    Witten, E.: Anti-de Sitter space and holography, Adv. Theoret. Math. Phys. 2 (1998), 253-291.Google Scholar
  20. 20.
    Dobrev, V. K.: Intertwining operator realization of the Ads/CFT correspondence, Nuclear Phys. B 553 (1999), 559-582.Google Scholar
  21. 21.
    Greenberg, O. W.: Generalized free fields and models of local field theory, Ann. Phys. 16 (1961), 158-176.Google Scholar

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© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. Dütsch
    • 1
  • K.-H. Rehren
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

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