Black holes, branes and superconformal symmetry

  • Renata Kallosh
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 525)


The main focus of this lecture is on extended objects in adS p+2×S d—p—2 bosonic backgrounds with unbroken supersymmetry. The backgrounds are argued to be exact, special consideration are given to the non-maximal supersymmetry case. The near horizon superspace construction is explained. The superconformal symmetry appears in the worldvolume actions as the superisometry of the near horizon superspace, like the superPoincaré symmetry of GS superstring and BST supermembrane in the flat superspace. The issues in gauge fixing of local kappa-symmetry are reviewed.

We describe the features of the gauge-fixed IIB superstring in adS 5×S 5 background with RR 5-form. From a truncated boundary version of it we derive an analytic N=2 off shell harmonic superspace of Yang-Mills theory. The reality condition of the analytic subspace, which includes the antipodal map on the sphere, has a simple meaning of the symmetry of the string action in the curved space. The relevant issues of black holes and superconformal mechanics are addressed.


Black Hole Vector Multiplet Black Hole Horizon Superconformal Algebra Superconformal Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Maldacena, The large N limit of superconformal field theories and supergravity, hep-th/9711200 (1997)Google Scholar
  2. 2.
    P. Claus, R. Kallosh, J. Kumar, P. K. Townsend and A. Van Proeyen, Conformal theory of M2, D3, M5 and ‘D1+D5’ branes, JHEP 06 (1998) 004; hep-th/9801206.CrossRefADSGoogle Scholar
  3. 3.
    T. Banks and M. B. Green, Nonperturbative Effects in AdS 5× S 5 String Theory and d=4 SUSY Yang-Mills, hep-th/9804170.Google Scholar
  4. 4.
    R. Kallosh and A. Rajaraman Vacua of M-theory and String Theory, Phys. Rev. D58 (1998) 125003 hep-th/9805041.ADSMathSciNetGoogle Scholar
  5. 5.
    R. Güven, Phys. Lett. 191B (1987) 265Google Scholar
  6. 5a.
    D. Amati and C. Klimčik, Phys. Lett 219B (1988) 443; G. T. Horowitz, in: Proceedings of Strings’ 90, College Station, Texas, March 1990 (World Scientific, 1991) and references therein.ADSGoogle Scholar
  7. 6.
    E. Cremmer and S. Ferrara, Formulation of Eleven-Dimensional Supergravity in Superspace, Phys. Lett. 91B (1980) 61.ADSMathSciNetGoogle Scholar
  8. 7.
    L. Brink and P. Howe, Eleven-dimensional Supergravity On the Mass Shell in Superspace, Phys. Lett. 91B (1980) 384.ADSGoogle Scholar
  9. 8.
    S. Ferrara, R. Kallosh and A. Strominger, Phys. Rev. D52 (1995) 5412; hep-th/9508072.ADSMathSciNetGoogle Scholar
  10. 9.
    J. Schwarz, Covariant field equations of chiral N=2, D=10 supergravity, Nucl. Phys. B226 (1983) 269.CrossRefADSGoogle Scholar
  11. 10.
    P. S. Howe and P. C. West, The Complete N=2, d=10 Supergravity, Nucl. Phys. B238 (1984) 181.CrossRefADSMathSciNetGoogle Scholar
  12. 11.
    G. W. Gibbons and P. K. Townsend, Vacuum interpolation in supergravity via super p-branes, Phys. Rev. Lett. 71 (1993) 3754; hep-th/9307049.zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 12.
    S. Ferrara and R. Kallosh, Supersymmetry and Attractors, Phys. Rev. D54 (1996) 1514; hep-th/9602136.ADSMathSciNetGoogle Scholar
  14. 13.
    G. L. Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black-hole entropy, hep-th/9812082.Google Scholar
  15. 14.
    J. M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M theory, J. High Energy Phys. 12 (1997) 2, hep-th/9711053CrossRefADSMathSciNetGoogle Scholar
  16. 14a.
    C. Vafa, Black holes and Calabi-Yau threefolds, Adv. Theor. Math. Phys. 2 (1998) 207, hep-th/9711067.zbMATHMathSciNetGoogle Scholar
  17. 15.
    R. Kallosh, J. Rahmfeld and A. Rajaraman, Near horizon superspace, JHEP 09 (1998) 002, hep-th/98-5217.CrossRefADSMathSciNetGoogle Scholar
  18. 16.
    R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5×S5 background, Nucl. Phys. B533 (1998) 109, hep-th/9805028; R.R. Metsaev and A.A. Tseytlin, Supersymmetric D3-brane action in AdS 5×S5, hep-th/9806095.CrossRefADSMathSciNetGoogle Scholar
  19. 17.
    P. Claus and R. Kallosh, Superisometries of the adS×S superspace, hep-th/9812087 (1998).Google Scholar
  20. 18.
    B. de Wit, K. Peeters, J. Plefka and A. Sevrin, The M-Theory Two-Brane in AdS 4 ×S 7 and AdS 7×S4, hep-th/9808052 (1998).Google Scholar
  21. 19.
    M.B. Green and J.H. Schwarz, Covariant description of superstrings, Phys. Lett. B136 (1984) 367; M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory, Cambridge University Press, 1987.Google Scholar
  22. 20.
    R. Kallosh, Superconformal actions in Killing gauge, hep-th/9807206.Google Scholar
  23. 21.
    H. Lü, C.N. Pope and J. Rahmfeld, A Construction of Killing Spinors on S n, hep-th/9805151 (1998).Google Scholar
  24. 22.
    P. Pasti, D. Sorokin, Mario Tonin, On gauge-fixed superbrane actions in ads superbackgrounds, hep-th/9809213.Google Scholar
  25. 23.
    R. Kallosh and J. Rahmfeld, The GS string action on AdS 5× S 5, hep-th/9808038.Google Scholar
  26. 24.
    R. Kallosh and A. Tseytlin, Simplifying Superstring Action on AdS 5×55, JHEP 10 (1998) 016, hep-th/9808088.CrossRefADSMathSciNetGoogle Scholar
  27. 25.
    G. Dall’Agata, D. Fabbri, C. Fraser, P. Fre, P. Termonia and M. Trigiante, The Osp(8/4) singleton action from the supermembrane, hep-th/98-7115.Google Scholar
  28. 26.
    I. Pesando, A kappa gauge fixed type IIB superstring action on AdS 5×S 5, hep-th/9808020.Google Scholar
  29. 27.
    M.T. Grisaru, P. Howe, L. Mezincescu, B. Nilsson and P.K. Townsend, N=2 superstrings in a supergravity background, Phys. Lett. B162 (1985) 116.ADSMathSciNetGoogle Scholar
  30. 28.
    I. Pesando, All Roads Lead to Rome: Supersolvables and Supercosets, hep-th/9808146.Google Scholar
  31. 29.
    P. Claus, R. Kallosh and J. Rahmfeld, Symmetries of the Boundary of AdS 5×S 5 and Harmonic Superspace, hep-th/9812114.Google Scholar
  32. 30.
    A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky and E. Sokatchev, Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quantum Grav. 1 (1984) 469.CrossRefADSMathSciNetGoogle Scholar
  33. 31.
    A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev, Harmonic superspace in action: general N=2 matter self-couplings, in Proceedings of the Trieste Spring School ’supersymmetry, supergravity, superstrings 86’, edited by B. de Wit, P. Fayet, M. Grisaru, WS, 1986.Google Scholar
  34. 32.
    P. Claus, M. Derix, R. Kallosh, J. Kumar, P.K. Townsend and A. Van Proeyen, Superconformal mechanics and black holes, Phys. Rev. Lett. 81 (1998) 4553, hep-th/9804177.zbMATHCrossRefADSMathSciNetGoogle Scholar
  35. 33.
    J.A. de Azcárraga, J.M. Izquierdo, J.C. Pérez-Bueno and P.K. Townsend, Superconformal mechanics, black holes and non-linear realizations, hep-th/9810230.Google Scholar
  36. 34.
    G.W. Gibbons and P.K. Townsend, Black Holes and Calogero Models, hep-th/9812034.Google Scholar
  37. 35.
    V. de Alfaro, S. Fubini and G. Furlan, Conformal Invariance in Quantum Mechanics, Nuovo. Cimento. 34A (1976) 569.ADSGoogle Scholar
  38. 35a.
    See also K. M. Case, Singular potentials, Phys. Rev. 80 (1950) 797.zbMATHCrossRefADSMathSciNetGoogle Scholar
  39. 36.
    V.P. Akulov and I.A. Pashnev, Quantum superconformal model in (1,2) space, Theor. Math. Phys. 56 (1983) 862CrossRefGoogle Scholar
  40. 36a.
    S. Fubini and E. Rabinovici, Superconformal Quantum Mechanics, Nucl. Phys. B245 (1984) 17.CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Renata Kallosh
    • 1
  1. 1.Physics DepartmentStanford UniversityStanfordUSA

Personalised recommendations