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Theoretical and Mathematical Physics

, Volume 182, Issue 1, pp 130–140 | Cite as

Symmetry orbits of supergravity black holes

  • K. S. StelleEmail author
Article
  • 68 Downloads

Abstract

Black-hole solutions of supergravity theories form families that realize the deep nonlinear “duality” symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e., BPS) solutions at the limits of such orbits. An important technique for analyzing such solution families uses timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. We characterize families of extremal or BPS solutions by nilpotent orbits under the duality symmetries, based on a trigraded or pentagraded decomposition of the corresponding duality-group algebra.

Keywords

black hole duality symmetry sigma model 

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References

  1. 1.
    A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1988); English transl.: L. D. Faddeev and A. A. Slavnov Gauge Fields: Introduction to Quantum Theory (Frontiers Phys., Vol. 83), Benjamin, Reading, Mass. (1991).zbMATHGoogle Scholar
  2. 2.
    A. A. Slavnov, Theor. Math. Phys., 10, 99–104 (1972).CrossRefMathSciNetGoogle Scholar
  3. 3.
    T. D. Bakeyev and A. A. Slavnov, Modern Phys. Lett. A, 11, 1539–1554 (1996); arXiv:hep-th/9601092v1 (1996).ADSCrossRefGoogle Scholar
  4. 4.
    A. A. Slavnov, Phys. Lett. B, 388, 147–153 (1996); arXiv:hep-th/9512101v1 (1995).ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. A. Slavnov, Theor. Math. Phys., 148, 1159–1167 (2006); arXiv:hep-th/0604052v1 (2006).CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    A. A. Slavnov, Phys. Lett. B, 217, 91–94 (1989).ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Neugebaur and D. Kramer, Ann. Phys. (Leipzig), 479, 62–71 (1969).CrossRefGoogle Scholar
  8. 8.
    P. Breitenlohner, D. Maison, and G. W. Gibbons, Commun. Math. Phys., 120, 295–333 (1988).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    G. Cl’emen and D. Gal’tsov, Phys. Rev. D, 54, 6136–6152 (1996); arXiv:hep-th/9607043v2 (1996); D. V. Gal’tsov and O. A. Rytchkov, Phys. Rev. D, 58, 122001 (1998); arXiv:hep-th/9801160v1 (1996).ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    E. Cremmer and B. Julia, Nucl. Phys. B, 159, 141–212 (1979).ADSCrossRefMathSciNetGoogle Scholar
  11. 11.
    B. de Wit, A. K. Tollsten, and H. Nicolai, Nucl. Phys. B, 392, 3–38 (1993); arXiv:hep-th/9208074v1 (1992).ADSCrossRefGoogle Scholar
  12. 12.
    P. Meessen and T. Ortin, Nucl. Phys. B, 749, 291–324 (2006); arXiv:hep-th/0603099v2 (2006).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    M. Cvetič and D. Youm, Phys. Rev. D, 53, R584–R588 (1996); arXiv:hep-th/9507090v2 (1995).ADSCrossRefGoogle Scholar
  14. 14.
    M. Cvetič and A. A. Tseytlin, Phys. Lett. B, 366, 95–103 (1996); arXiv:hep-th/9510097v4 (1995).ADSCrossRefMathSciNetGoogle Scholar
  15. 15.
    J. Eells Jr. and J. H. Sampson, Am. J. Math., 86, 109–160 (1964).CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    G. Bossard, H. Nicolai, and K. S. Stelle, JHEP, 0907, 003 (2009); arXiv:0902.4438v3 [hep-th] (2009).ADSCrossRefMathSciNetGoogle Scholar
  17. 17.
    G. Bossard, H. Nicolai, and K. S. Stelle, Gen. Rel. Grav., 41, 1367–1379 (2009); arXiv:0809.5218v2 [hep-th] (2008).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    J. Ehlers, “Konstruktion und Charakterisierungen von Lösungen der Einsteinschen Gravitationsgleichungen,” Dissertation, University of Hamburg, Hamburg (1957).Google Scholar
  19. 19.
    M. Günaydin, G. Sierra, and P. K. Townsend, Phys. Lett. B, 133, 72–76 (1983).ADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    D. Ž. Dokovi’c, Represent. Theory, 5, 17–42 (2001); J. Lie Theory, 10, 491–510 (2000); 11, 381–413 (2001); Asian J. Math., 5, 561–584 (2001).CrossRefMathSciNetGoogle Scholar
  21. 21.
    E. Cremmer, H. Lü, C. N. Pope, and K. S. Stelle, Nucl. Phys. B, 520, 132–156 (1998); arXiv:hep-th/9707207v2 (1997).ADSCrossRefzbMATHGoogle Scholar
  22. 22.
    G. Bossard and H. Nicolai, Gen. Rel. Grav., 42, 509–537 (2010); arXiv:0906.1987v2 [hep-th] (2009).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    G. Bossard and C. Ruef, Gen. Rel. Grav., 44, 21–66 (2012); arXiv:1106.5806v1 [hep-th] (2011).ADSCrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.The Blackett LaboratoryImperial College LondonLondonUK

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