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AdS/CFT Correspondence in the Euclidean Context

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Abstract

We study two possible prescriptions for the AdS/CFT correspondence by means of functional integrals. The considerations are non-perturbative and reveal certain divergencies which turn out to be harmless, in the sense that reflection positivity and conformal invariance are not destroyed.

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References

  1. Berenstein C.A. and Gay R. (1991). Complex Variables. Springer, New York

    Google Scholar 

  2. Berezanskii, Iu. M., Kondratiev, Iu. M.: Spectral Methods in Infinite-Dimensional Analysis. Vol. 1, Dordrecht: Kluwer Academic Publishers, 1995

  3. Bertola M., Bros J., Moschella U. and Schaeffer R. (2000). Decomposing quantum fields on branes. Nucl. Phys. B 581: 575–603

    Article  ADS  MathSciNet  Google Scholar 

  4. Bogachev, V.I.: Gaussian Measures. RI: Amer. Math. Soc., Providence, 1998 (translated from Russian)

  5. Bros J., Epstein H. and Moschella U. (2002). Towards a general theory of quantized fields on the anti-de Sitter spacetime. Commun. Math. Phys. 231: 481–528

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Dimock J. (2004). Markov quantum fields on a manifold. Rev. Math. Phys. 16: 243–256

    Article  MATH  MathSciNet  Google Scholar 

  7. Dimock J. and Glimm J. (1974). Measures on Schwartz distribution space and applications to P(φ)2 field theories. Adv. Math. 12: 58–83

    Article  MATH  MathSciNet  Google Scholar 

  8. Dobrev V.K. (2004). Intertwining operator realization of the AdS/CFT correspondence. Nucl. Phys. B 553: 559–582

    ADS  MathSciNet  Google Scholar 

  9. Dütsch M. and Rehren K.H. (2002). A comment on the dual field in the AdS-CFT correspondence. Lett. Math. Phys. 62: 171–184

    Article  MATH  MathSciNet  Google Scholar 

  10. Eguchi, M., Okamoto, K.: The Fourier transform of the Schwartz space on a symmetric space. Proc. Japan Acad. 53, Ser. A, 237-241 (1977)

  11. Gelfand, I.M., Shilov, G.E.: Generalized Functions, Vol.1. Properties and Operations. New York-London: Academic Press, 1964 (1977)

  12. Glimm, J., Jaffe, A.: Quantum Physics. A Functional Integral Point of View, 2nd edition. New-York: Springer, 1987

    Google Scholar 

  13. Gottschalk, H.: Die Momente gefalteten Gauß-Poissonschen weißen Rauschens als Schwingerfunktionen. Diploma thesis, Bochum, 1995

  14. Gubser S.S., Klebanov I.R. and Polyakov A.M. (1998). Gauge theory correlators from noncritical string theory. Phys. Lett. B 428: 105–114

    Article  ADS  MathSciNet  Google Scholar 

  15. Haba Z. (2000). Quantum field theory on manifolds with a boundary. J. Phys. A 38: 10393–10401

    ADS  MathSciNet  Google Scholar 

  16. Helgason, S.: Groups and Geometric Analysis. Mathematical Surveys and Monographs, Vol. 83, Providence, RI: Amer. Math. Soc., 2000

  17. Jaffee, A., Ritter, G.: Quantum field theory on curved backgrounds II: Spacetime symmetries. http://arxiv.org/list/hep-th/0704.0052, 2007

  18. Kniemeyer, O.: Untersuchungen am erzeugenden Funktional der AdS-CFT-Korrespondenz. Diploma thesis, Univ. Göttingen, 2002

  19. Hong L. and Tseytlin A.A. (1999). On four point functions in the CFT/AdS correspondence. Phys. Rev. D 59: 086002

    Article  ADS  MathSciNet  Google Scholar 

  20. Maldacena J. (1998). The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2: 231–252

    MATH  MathSciNet  Google Scholar 

  21. Mück W. and Wiswanathan K.S. (1999). Regular and irregular boundary conditions in the AdS/CFT Correspondence. Phys. Rev. D 60: 081901

    Article  ADS  MathSciNet  Google Scholar 

  22. Osterwalder K. and Schrader R. (1973). Axioms for Euclidean Green’s functions. Commun. Math. Phys. 31: 83–112

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. Osterwalder K. and Schrader R. (1975). Axioms for Euclidean Green’s functions. II. With an appendix by S. Summers. Commun. Math. Phys. 42: 281–305

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. Rehren K.-H (2000). Algebraic holography. Ann. Henri Poincarè 1: 607–623

    Article  MATH  MathSciNet  Google Scholar 

  25. Rehren, K.-H.: QFT lectures on AdS-CFT. In: Proc. of 3rd Summer School on Modern Math. Phys., Belgrade:Inst. of Phys., pp. 95–118, 2005

  26. Strichartz R.S. (1983). Analysis of the Laplacian on the complete Riemannian manifold. J. Funct. Anal. 52: 48–79

    Article  MATH  MathSciNet  Google Scholar 

  27. Tartaru D. (2000). Strichartz estimates in the hyperbolic space and global existence for the nonlinear wave equation. Trans. Am. Math. Soc. 353: 795–807

    Article  Google Scholar 

  28. Weidmann, J.: Lineare Operatoren. B.G. Teubner, Stuttgart, 1976

  29. Witten E. (1998). Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2: 253–291

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut für angewandte Mathematik, Universität Bonn, Bonn, Germany

    Hanno Gottschalk

  2. Dipartimento di Matematica e Informatica, Università di Camerino, Camerino, Italy

    Horst Thaler

Authors
  1. Hanno Gottschalk
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  2. Horst Thaler
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Correspondence to Horst Thaler.

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Communicated by J.Z. Imbrie

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Gottschalk, H., Thaler, H. AdS/CFT Correspondence in the Euclidean Context. Commun. Math. Phys. 277, 83–100 (2008). https://doi.org/10.1007/s00220-007-0358-4

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  • DOI: https://doi.org/10.1007/s00220-007-0358-4

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