Advertisement

On the Classification of Two Center Orbits for Magical Black Holes

  • Laura Andrianopoli
  • Riccardo D’Auria
  • Sergio Ferrara
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 142)

Abstract

We report on recent work [4] concerning the determination of the two-centered generic charge orbits of magical \(\mathcal{N} = 2\) and maximal \(\mathcal{N} = 8\) supergravity theories in four dimensions.

Keywords

Black Hole Jordan Algebra Supergravity Theory Extremal Black Hole Charge Vector 
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.

Notes

Acknowledgements

The present contribution is based on [4] made in collaboration with Alessio Marrani and Mario Trigiante. The work of S. F. is supported by the ERC Advanced Grant no. 226455, “Supersymmetry, Quantum Gravity and Gauge Fields” (SUPERFIELDS). The work of L.A. and R.D’A. is supported in part by the MIUR-PRIN contract 2009-KHZKRX.

References

  1. 1.
    L. Andrianopoli, R. D’Auria, S. Ferrara, U-invariants, black hole entropy and fixed scalars. Phys. Lett. B403, 12 (1997). hep-th/9703156 Google Scholar
  2. 2.
    L. Andrianopoli, R. D’Auria, S. Ferrara, M. Trigiante, Extremal black holes in supergravity. Lect. Notes Phys. 737, 661 (2008). hep-th/0611345 Google Scholar
  3. 3.
    L. Andrianopoli, R. D’Auria, S. Ferrara, P.A. Grassi, M. Trigiante, Exceptional \(\mathcal{N} = 6\) and \(\mathcal{N} = 2\) AdS 4 supergravity, and zero-center modules. J. High Energy Phys. 0904, 074 (2009). arXiv:0810.1214 (hep-th) Google Scholar
  4. 4.
    L. Andrianopoli, R. D’Auria, S. Ferrara, A. Marrani, M. Trigiante, Two-centered magical charge orbits. J. High Energy Phys. 1104, 041 (2011). (arXiv:1101.3496 (hep-th))Google Scholar
  5. 5.
    B. Bates, F. Denef, Exact Solutions for Supersymmetric Stationary Black Hole Composites. J. High Energy Phys. 1111, 127 (2011). hep-th/0304094 Google Scholar
  6. 6.
    J.C. Baez, The octonions. Bull. Am. Math. Soc. 39, 145 (2001). math/0105155 Google Scholar
  7. 7.
    S. Bellucci, S. Ferrara, M. Günaydin, A. Marrani, Charge orbits of symmetric special geometries and attractors. Int. J. Mod. Phys. A21, 5043 (2006). hep-th/0606209 Google Scholar
  8. 8.
    L. Borsten, D. Dahanayake, M.J. Duff, W. Rubens, Black holes admitting a freudenthal dual. Phys. Rev. D80, 026003 (2009). arXiv:0903.5517 (hep-th) Google Scholar
  9. 9.
    G. Bossard, 1∕8 BPS Black Hole Composites. arXiv:1001.3157 (hep-th) Google Scholar
  10. 10.
    A. Castro, J. Simon, Deconstructing the D0-D6 system. J. High Energy Phys. 0905, 078 (2009). arXiv:0903.5523 (hep-th) Google Scholar
  11. 11.
    E. Cremmer, B. Julia, The \(\mathcal{N} = 8\) supergravity theory. 1. The lagrangian. Phys. Lett. B80, 48 (1978); E. Cremmer, B. Julia, The SO(8) supergravity. Nucl. Phys. B159, 141 (1979)Google Scholar
  12. 12.
    M. Cvetic, D. Youm, Dyonic BPS saturated black holes of heterotic string on a six torus. Phys. Rev. D53, 584 (1996), hep-th/9507090; M. Cvetic, A.A. Tseytlin, General class of BPS saturated dyonic black holes as exact superstring solutions. Phys. Lett. B366, 95 (1996). hep-th/9510097; M. Cvetic, A.A. Tseytlin, Solitonic strings and BPS saturated dyonic black holes. Phys. Rev. D53, 5619 (1996); Erratum-ibid. D55, 3907 (1997), hep-th/9512031 Google Scholar
  13. 13.
    J.R. David, On walls of marginal stability in \(\mathcal{N} = 2\) string theories. J. High Energy Phys. 0908, 054 (2009). arXiv:0905.4115 (hep-th) Google Scholar
  14. 14.
    B. de Wit, H. Samtleben, M. Trigiante, On lagrangians and gaugings of maximal supergravities. Nucl. Phys. B655, 93 (2003). hep-th/0212239 Google Scholar
  15. 15.
    B. de Wit, F. Vanderseypen, A. Van Proeyen, Symmetry structures of special geometries. Nucl. Phys. B400, 463 (1993). hep-th/9210068 Google Scholar
  16. 16.
    F. Denef, Supergravity flows and D-brane stability. J. High Energy Phys. 0008, 050 (2000). hep-th/0005049 Google Scholar
  17. 17.
    F. Denef, G.W. Moore, Split States, Entropy Enigmas, Holes and Halos. hep-th/0702146; J. High Energy Phys. 1111, 129 (2011). F. Denef, D. Gaiotto, A. Strominger, D. Van den Bleeken, X. Yin, Black Hole Deconstruction. hep-th/0703252; J. High Energy Phys. 1203, 071 (2012). F. Denef, G.W. Moore, How many black holes fit on the head of a pin? Gen. Relat. Gravit. 39, 1539 (2007). arXiv:0705.2564 (hep-th) Google Scholar
  18. 18.
    F. Denef, B.R. Greene, M. Raugas, Split attractor flows and the spectrum of BPS D-branes on the quintic. J. High Energy Phys. 0105, 012 (2001). hep-th/0101135 Google Scholar
  19. 19.
    M.J. Duff, J.T. Liu, J. Rahmfeld, Four-dimensional string/string/string triality. Nucl. Phys. B459, 125 (1996). hep-th/9508094 Google Scholar
  20. 20.
    S. Ferrara, M. Günaydin, Orbits of exceptional groups, duality and BPS states in string theory. Int. J. Mod. Phys. A13, 2075 (1998). hep-th/9708025 Google Scholar
  21. 21.
    S. Ferrara, A. Marrani, Matrix norms, BPS bounds and marginal stability in \(\mathcal{N} = 8\) supergravity. J. High Energy Phys. (2010, in press). arXiv:1009.3251 (hep-th) Google Scholar
  22. 22.
    S. Ferrara, R. Kallosh, A. Strominger, \(\mathcal{N} = 2\) extremal black holes. Phys. Rev. D52, 5412 (1995). hep-th/9508072; A. Strominger, Macroscopic entropy of \(\mathcal{N} = 2\) extremal black holes. Phys. Lett. B383, 39 (1996). hep-th/9602111; S. Ferrara, R. Kallosh, Supersymmetry and attractors. Phys. Rev. D54, 1514 (1996). hep-th/9602136; S. Ferrara, R. Kallosh, Universality of supersymmetric attractors. Phys. Rev. D54, 1525 (1996). hep-th/9603090 Google Scholar
  23. 23.
    S. Ferrara, G.W. Gibbons, R. Kallosh, Black holes and critical points in moduli space. Nucl. Phys. B500, 75 (1997). hep-th/9702103 Google Scholar
  24. 24.
    S. Ferrara, E.G. Gimon, R. Kallosh, Magic supergravities, \(\mathcal{N} = 8\) and black hole composites. Phys. Rev. D74, 125018 (2006). hep-th/0606211 Google Scholar
  25. 25.
    S. Ferrara, A. Marrani, E. Orazi, Split Attractor Flow in \(\mathcal{N} = 2\)  Minimally Coupled Supergravity. arXiv:1010.2280 (hep-th), Nucl. Phys. B846, 512–541 (2011)Google Scholar
  26. 26.
    S. Ferrara, A. Marrani, E. Orazi, R. Stora, A. Yeranyan, Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants. arXiv:1011.5864 (hep-th), J. Math. Phys. 062302, 52 (2011)Google Scholar
  27. 27.
    S. Ferrara, A. Marrani, A. Yeranyan, On Invariant Structures of Black Hole Charges. arXiv:1110.4004 (hep-th), J. High Energy Phys. 1202, 071 (2012).Google Scholar
  28. 28.
    D. Gaiotto, W.W. Li, M. Padi, Non-supersymmetric attractor flow in symmetric spaces. J. High Energy Phys. 0712, 093 (2007). arXiv:0710.1638 (hep-th) Google Scholar
  29. 29.
    E.G. Gimon, F. Larsen, J. Simon, Constituent model of extremal non-BPS black holes. J. High Energy Phys. 0907, 052 (2009). arXiv:0903.0719 (hep-th) Google Scholar
  30. 30.
    M. Günaydin, Lectures on Spectrum Generating Symmetries and U-Duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace. arXiv:0908.0374 (hep-th) Google Scholar
  31. 31.
    M. Günaydin, G. Sierra, P.K. Townsend, Exceptional supergravity theories and the magic square. Phys. Lett. B133, 72 (1983); M. Günaydin, G. Sierra, P.K. Townsend, The geometry of \(\mathcal{N} = 2\) Maxwell-Einstein supergravity and Jordan Algebras. Nucl. Phys. B242, 244 (1984)Google Scholar
  32. 32.
    C. Hull, P.K. Townsend, Unity of superstring dualities. Nucl. Phys. B438, 109 (1995). hep-th/9410167 Google Scholar
  33. 33.
    V.G. Kaç, Some remarks on nilpotent orbits. J. Algebr. 64, 190–213 (1980)Google Scholar
  34. 34.
    P. Levay, Two-center black holes, qubits and elliptic curves. Phys. Rev. D 84, 025023 (2011). arXiv:1104.0144 (hep-th) Google Scholar
  35. 35.
    J.F. Luciani, Coupling of O(2) supergravity with several vector multiplets. Nucl. Phys. B132, 325 (1978)Google Scholar
  36. 36.
    A. Marrani, E. Orazi, F. Riccioni, Exceptional reductions. arXiv:1012.5797v1 (hep-th), J. Phys. A. A44, 155207 (2011)Google Scholar
  37. 37.
    D. Roest, H. Samtleben, Twin supergravities. Class. Quantum Gravity 26, 155001 (2009). arXiv:0904.1344(hep-th) Google Scholar
  38. 38.
    R. Slansky, Group theory for unified model building. Phys. Rep. 79, 1 (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Laura Andrianopoli
    • 1
    • 2
  • Riccardo D’Auria
    • 1
    • 2
  • Sergio Ferrara
    • 3
  1. 1.Dipartimento di FisicaPolitecnico di TorinoTorinoItaly
  2. 2.INFNSezione di TorinoTorinoItaly
  3. 3.Physics Department, Theory UnitCERNGeneva 23Switzerland

Personalised recommendations