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Branes in Anti-de Sitter Space-Time

  • M. Trigiante

Abstract

An intense study of the relationship between certain quantum theories of gravity realized on curved backgrounds and suitable gauge theories, has been initiated by a remarkable conjecture put forward by Maldacena almost one year ago. Among the possible curved vacua of superstring or M-theory, spaces having the form of an anti-de Sitter space-time times a compact Einstein manifold, have been playing a special role in this correspondence, since the quantum theory realized on them, in the original formulation of the conjecture, was identified with the effective superconformai theory on the world volume of parallel p-branes set on the boundary of such a space (holography). An important step in verifying such a conjecture and eventually generalizing it, consists in a precise definition of the objects entering both sides of the holographic correspondence. Indeed in the most general case it turns out that important features of the field theory on the boundary of the curved background, identified with the quantum theory of gravity in the bulk, are encoded in the dynamics of the coinciding parallel p-branes set on the boundary of the same space. The study of p-brane dynamics in curved space-times which are vacua of superstring or M-theory, turns out therefore to be a relevant issue in verifying the existence of the holographic correspondence. In the present paper, besides providing a hopefully elementary introduction to Maldacena’s duality, I shall deal in a tentatively self-contained way with a particular aspect of the problem of p-brane dynamics in anti-de Sitter space-time, discussing some recent results towards the definition of a method for retrieving important features of the field theory on the boundary from the quantization for small oscillations of the world-volume theory of a single p-brane around the same boundary.

Keywords

Target Space Closed String Einstein Manifold Unitary Irreducible Representation Curve Background 
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References

  1. 1.
    Green M., Schwarz J., Witten E. (1987): Superstring Theory. Vols. 1, 2. Cambridge University Press, CambridgeMATHGoogle Scholar
  2. 2.
    Polchinski J. (1997): String Theory. Cambridge University Press, CambridgeGoogle Scholar
  3. 3.
    Kallosh R., Tseytlin A. (1998): Simplifying superstring action on AdS(5) × S(5). JHEP 9810, 016; Metsaev R., Tseytlin A. (1998): Supersymmetric D3 brane action in AdS(5) × S**(5). Phys. Lett. B 436, 281–288; Rayaraman A., Rozali M. (1999): On the quantization of the GS string on AdS(5) × S(5). Phys. Lett. B 468, 58; Pesando I. (1999): On the quantization of the GS type IIB superstring action on AdS(3) × S(3) with NSNS flux, hep-th/9903086MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Maldacena J. (1998): Adv. Theor. Math. Phys. 2, 231–252MathSciNetADSMATHGoogle Scholar
  5. 5.
    Duff M.: Anti-de Sitter space, branes, singletons, superconformai field theories and all that, hep-th/980810Google Scholar
  6. 6.
    Schwarz J. (1997): Nucl. Phys. Proc. Suppl. B 55, 1–32; Sen A. (1997): Nucl. Phys. Proc. Suppl. 58, 5–19ADSCrossRefGoogle Scholar
  7. 7.
    Hull CM., Townsend P.K. (1995): Nucl. Phys. B 438, 109MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Polchinski J. (1996): TASI lectures on D-branes, in Fields, Strings and Duality, ed. by C. Efthimion, B. Greene, World Scientific, Singapore, pp. 293–356Google Scholar
  9. 9.
    Lu H., Pope C.N., Sezgin E., Stelle K.S. (1995): Stainless super p-branes. Nucl. Phys. B 456, 669; Lu H., Pope C.N., Stelle K.S. (1996): Vertical Versus Diagonal Dimensional Reduction for p-branes. Nucl. Phys. B 481, 313–331; Duff M.J., Lu H., Pope C.N. (1996): The black branes of M-theory. Phys. Lett. B 382, 73–80; Lu H., Pope C.N., Stelle K.S. (1996): Weyl Group Invariance and p-brane Multiplets. Nucl. Phys. B 476, 89–117MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Fré P. (1997): Supersymmetry and first order equations for extremal states: Monopoles, hyperinstantons, black holes and p-branes. Nucl. Phys. Proc. Suppl. 57, 52–64ADSMATHCrossRefGoogle Scholar
  11. 11.
    Kallosh R., Rajaraman A. (1998): Phys. Rev. D 58, 125003MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Castellani L., Ceresole A., D’Auria R., Ferrara S., Fré P., Trigiante M. (1998): Nucl. Phys. B 527, 142–170ADSMATHCrossRefGoogle Scholar
  13. 13.
    Acharya B.S., Figueroa-O’Farrill J.M., Hull CM., Spence B. (1999): Branes at conical singularities and holography. Adv. Theor. Math. Phys. 2, 1249–1286MathSciNetGoogle Scholar
  14. 14.
    Witten E. (1998): Adv. Theor. Math. Phys. 2, 253MathSciNetADSMATHGoogle Scholar
  15. 15.
    Freund P.G.O., Rubin M.A. (1980): Phys. Lett. B 97, 233; Duff M.J., Nilsson B.E.W., Pope C.N. (1986): Phys. Rep. 130, 1; Englert F (1982): Phys. Lett. B 119, 339; Castellani L., D’Auria R., Frè P. (1984): Nucl. Phys. 239, 610; Castellani L., Romans L. J., Warner N.R (1984): Nucl. Phys. B 241, 429; de Wit B., Nicolai H. (1984): Nucl. Phys. B 231, 506; de Wit B., Nicolai H. (1987): Nucl. Phys. B 281, 211MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Dorey N., Hollowood T. J., Khoze V.V., Mattis M.P., Vandoren S. (1999): Multi-instanton calculus and the AdS/CFT correspondence in N = 4 superconformai field theory. Nucl. Phys. B 552, 88–168. hep-th/9901128; Dorey N., Hollowood T.J., Khoze V.V, Mattis M.P, Vandoren D. (1999): Multi-instantons and Maldacena’s conjecture, JHER 9906:023. hep-th/9810243MathSciNetADSMATHCrossRefGoogle Scholar
  17. 17.
    Dirac P.A.M. (1963): J. Math. Phys. 4, 901MathSciNetADSMATHCrossRefGoogle Scholar
  18. 18.
    Fronsdal C. (1982): Phys. Rev. D 26; Flato M., Fronsdal C. (1981): J. Math. Phys. 22, 1100; Angelopoulos E., Flato M., Fronsdal C, Steinheimer D. (1981): Phys. Rev. D 23, 1278; Bergshoeff E., Salam A., Sezgin E., Tanii Y. (1987): Phys. Lett. B 205, 237; Bergshoeff E., Duff M.J., Pope C.N., Sezgin E. (1987): Phys. Lett. B 199, 69; Bergshoeff E., Duff M.J., Pope C.N., Sezgin E. (1989): Phys. Lett. B 224, 71Google Scholar
  19. 19.
    Ferrara S., Fronsdal C. (1998): Phys. Lett. B 433, 19; Ferrara S., Fronsdal C, Zaffaroni A. (1998): Nucl. Phys. B 532, 153; Andrianopoli L., Ferrara S. (1999): Short and long SU(2, 2/4) multiplets in the AdS/CFT correspondence. Lett. Math. Phys. 48, 145–161MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Dall’Agata G., Fabbri D., Fraser C, Fre P., Termonia P., Trigiante M. (1999): Nucl. Phys. B 542, 157–194MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Kallosh R. (1998): Superconformai actions in killing gauge, hep-th/9807206Google Scholar
  22. 22.
    Pesando I. (1998): All roads lead to Rome: Supersolvable and supercosets. Mod. Phys. Lett. A 14, 343–348; Pesando I. (1998): JHEP 9811, 002MathSciNetADSCrossRefGoogle Scholar

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© Springer-Verlag Italia 2000

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  • M. Trigiante

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