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Charge Orbits and Moduli Spaces of Black Hole Attractors

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Supersymmetry in Mathematics and Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2027))

Abstract

We report on the theory of “large” U-duality charge orbits and related “moduli spaces” of extremal black hole attractors in N = 2, d = 4 Maxwell–Einstein supergravity theories with symmetric scalar manifolds, as well as in N ≥ 3-extended, d = 4 supergravities.

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References

  1. S. Ferrara, R. Kallosh, A. Strominger, N= 2 extremal black holes. Phys. Rev. D52, 5412 (1995). hep-th/9508072

    Google Scholar 

  2. A. Strominger, Macroscopic entropy of N= 2 extremal black holes. Phys. Lett. B383, 39 (1996). hep-th/9602111.

    Google Scholar 

  3. S. Ferrara, R. Kallosh, Supersymmetry and attractors. Phys. Rev. D54, 1514 (1996). hep-th/9602136

    Google Scholar 

  4. S. Ferrara, R. Kallosh, Universality of supersymmetric attractors. Phys. Rev. D54, 1525 (1996). hep-th/9603090

    Google Scholar 

  5. 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 

  6. S. Bellucci, S. Ferrara, A. Marrani, Supersymmetric Mechanics, Vol. 2: The Attractor Mechanism and Space-Time Singularities. Lect. Notes Phys., vol. 701 (Springer, Heidelberg, 2006)

    Google Scholar 

  7. B. Pioline, Lectures on black holes, topological strings and quantum attractors. Class. Quant. Grav. 23, S981 (2006). hep-th/0607227

    Google Scholar 

  8. L. Andrianopoli, R. D’Auria, S. Ferrara, M. Trigiante, Extremal Black Holes in Supergravity. Lect. Notes Phys., vol. 737 (Springer, Heidelberg, 2008), p. 661. hep-th/0611345

    Google Scholar 

  9. A. Sen, Black hole entropy function, attractors and precision counting of microstates. Gen. Rel. Grav. 40, 2249 (2008). arXiv:0708.1270

    Google Scholar 

  10. S. Bellucci, S. Ferrara, R. Kallosh, A. Marrani, Extremal Black Hole and Flux Vacua Attractors. Lect. Notes Phys., vol. 755 (Springer, Heidelberg, 2008), p. 115. arXiv:0711.4547

    Google Scholar 

  11. S. Ferrara, K. Hayakawa, A. Marrani, Erice lectures on black holes and attractors. Fortsch. Phys. 56, 993 (2008). arXiv:0805.2498.

    Google Scholar 

  12. S. Bellucci, S. Ferrara, M. Günaydin, A. Marrani, SAM lectures on extremal Black holes in d = 4 extended supergravity. arXiv:0905.3739

    Google Scholar 

  13. M. Günaydin, Lectures on spectrum generating symmetries and U-duality in supergravity, extremal black holes, quantum attractors and harmonic superspace. arXiv:0908.0374

    Google Scholar 

  14. A. Ceresole, S. Ferrara, Black holes and attractors in supergravity. arXiv:1009.4715

    Google Scholar 

  15. L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Frè, T. Magri, N= 2 Supergravity and N= 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map. J. Geom. Phys. 23, 111 (1997). hep-th/9605032

    Google Scholar 

  16. M.J. Duff, String triality, black hole entropy and Cayley’s hyperdeterminant. Phys. Rev. D76, 025017 (2007). hep-th/0601134; See e.g. the following papers (and Refs. therein)

    Google Scholar 

  17. R. Kallosh, A. Linde, Strings, black holes, and quantum information. Phys. Rev. D73, 104033 (2006). hep-th/0602061

    Google Scholar 

  18. M.J. Duff, S. Ferrara, Black hole entropy and quantum information. Lect. Notes Phys. 755, 93 (2008). arXiv:hepth/0612036

    Google Scholar 

  19. L. Borsten, D. Dahanayake, M.J. Duff, H. Ebrahim, W. Rubens, Black holes, Qubits and Octonions. Phys. Rept. 471, 113 (2009). arXiv:0809.4685 [hep-th]

    Google Scholar 

  20. P. Levay, STU black holes as four qubit systems. Phys. Rev. D82, 026003 (2010). arXiv: 1004.3639 [hep-th]

    Google Scholar 

  21. L. Borsten, D. Dahanayake, M.J. Duff, A. Marrani, W. Rubens, Four-Qubit entanglement from string theory. Phys. Rev. Lett. 105, 100507 (2010). arXiv:1005.4915 [hep-th]

    Google Scholar 

  22. G.W. Gibbons, C.M. Hull, A Bogomol’ny bound for general relativity and solitons in N= 2 supergravity. Phys. Lett. B109, 190 (1982)

    MathSciNet  Google Scholar 

  23. G.W. Gibbons, P.K. Townsend, Vacuum interpolation in supergravity via super-p-branes. Phys. Rev. Lett. 71, 3754 (1993). hep-th/9307049

    Google Scholar 

  24. R. Arnowitt, S. Deser, C.W. Misner, in The Dynamics of General Relativity, ed. by L. Witten. Gravitation: An Introduction to Current Research (Wiley, New York, 1962)

    Google Scholar 

  25. B. Bertotti, Uniform electromagnetic field in the theory of general relativity. Phys. Rev. 116, 1331 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  26. I. Robinson, Bull. Acad. Polon. 7, 351 (1959)

    MATH  Google Scholar 

  27. J.D. Bekenstein, Phys. Rev. D7, 2333 (1973)

    MathSciNet  Google Scholar 

  28. S.W. Hawking, Phys. Rev. Lett. 26, 1344 (1971)

    Article  Google Scholar 

  29. C. DeWitt, B.S. DeWitt, Black Holes (Les Houches 1972) (Gordon and Breach, New York, 1973)

    Google Scholar 

  30. S.W. Hawking, Nature 248, 30 (1974)

    Article  Google Scholar 

  31. S.W. Hawking, Comm. Math. Phys. 43, 199 (1975)

    Article  MathSciNet  Google Scholar 

  32. J.F. Luciani, Coupling of O(2) supergravity with several vector multiplets. Nucl. Phys. B132, 325 (1978)

    Article  MathSciNet  Google Scholar 

  33. L. Castellani, A. Ceresole, S. Ferrara, R. D’Auria, P. Fré, E. Maina, The complete N= 3 matter coupled supergravity. Nucl. Phys. B268, 317 (1986)

    Article  Google Scholar 

  34. C. Hull, P.K. Townsend, Unity of superstring dualities. Nucl. Phys. B438, 109 (1995). hep-th/9410167

    Google Scholar 

  35. 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 

  36. R. D’Auria, S. Ferrara, M.A. Lledó, On central charges and Hamiltonians for 0 -brane dynamics. Phys. Rev. D60, 084007 (1999). hep-th/9903089

    Google Scholar 

  37. S. Ferrara, J.M. Maldacena, Branes, central charges and U -duality invariant BPS conditions. Class. Quant. Grav. 15, 749 (1998). hep-th/9706097

    Google Scholar 

  38. M. Günaydin, G. Sierra, P.K. Townsend, Exceptional supergravity theories and the magic square. Phys. Lett. B133, 72 (1983)

    Google Scholar 

  39. M. Günaydin, G. Sierra, P.K. Townsend, The geometry of N = 2 Maxwell–Einstein supergravity and Jordan algebras. Nucl. Phys. B242, 244 (1984)

    Article  Google Scholar 

  40. M. Günaydin, G. Sierra, P.K. Townsend, Gauging the d = 5 Maxwell–Einstein supergravity theories: More on Jordan algebras. Nucl. Phys. B253, 573 (1985)

    Article  Google Scholar 

  41. E. Cremmer, A. Van Proeyen, Classification of Kähler manifolds in N = 2 vector multiplet supergravity couplings. Class. Quant. Grav. 2, 445 (1985)

    Article  MATH  Google Scholar 

  42. B. de Wit, F. Vanderseypen, A. Van Proeyen, Symmetry structures of special geometries. Nucl. Phys. B400, 463 (1993). hep-th/9210068

    Google Scholar 

  43. S. Ferrara, A. Marrani, in Symmetric Spaces in Supergravity, ed. by D. Babbitt, V. Vyjayanthi, R. Fioresi. Symmetry in Mathematics and Physics, Contemporary Mathematics, vol. 490 (American Mathematical Society, Providence, 2009). arXiv:0808.3567

    Google Scholar 

  44. 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 

  45. S. Ferrara, A. Gnecchi, A. Marrani, d = 4 Attractors, effective horizon radius and fake supergravity. Phys. Rev. D78, 065003 (2008). arXiv:0806.3196

    Google Scholar 

  46. P. Jordan, J. Von Neumann, E. Wigner, On an algebraic generalization of the quantum mechanical formalism. Ann. Math. 35, 29 (1934)

    Article  Google Scholar 

  47. N. Jacobson, Ann. Math. Soc. Coll. Publ. 39 (1968)

    Google Scholar 

  48. M. Günaydin, Exceptional realizations of lorentz group: Supersymmetries and leptons. Nuovo Cimento A29, 467 (1975)

    Google Scholar 

  49. M. Günaydin, C. Piron, H. Ruegg, Moufang plane and Octonionic quantum mechanics. Comm. Math. Phys. 61, 69 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  50. H. Freudenthal, Proc. Konink. Ned. Akad. Wetenschap A62, 447 (1959)

    Google Scholar 

  51. B.A. Rozenfeld, Dokl. Akad. Nauk. SSSR 106, 600 (1956)

    MathSciNet  MATH  Google Scholar 

  52. J. Tits, Mem. Acad. Roy. Belg. Sci. 29, 3 (1955)

    MathSciNet  Google Scholar 

  53. L. Andrianopoli, R. D’Auria, S. Ferrara, U Duality and central charges in various dimensions revisited. Int. J. Mod. Phys. A13, 431 (1998). hep-th/9612105

    Google Scholar 

  54. S. Ferrara, E.G. Gimon, R. Kallosh, Magic supergravities, N= 8 and black hole composites. Phys. Rev. D74, 125018 (2006). hep-th/0606211

    Google Scholar 

  55. D. Roest, H. Samtleben, Twin supergravities. Class. Quant. Grav. 26, 155001 (2009). arXiv:0904.1344

    Google Scholar 

  56. R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (Dover, NY, 2006)

    Google Scholar 

  57. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, New York, 1978)

    MATH  Google Scholar 

  58. R. Slansky, Group theory for unified model building. Phys. Rep. 79, 1 (1981)

    Article  MathSciNet  Google Scholar 

  59. S. Ferrara, R. Kallosh, On N = 8 attractors. Phys. Rev. D73, 125005 (2006). hep-th/0603247

    Google Scholar 

  60. S. Ferrara, A. Marrani, N= 8 non-BPS attractors, fixed scalars and magic supergravities. Nucl. Phys. B788, 63 (2008). arXiV:0705.3866

    Google Scholar 

  61. 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 

  62. S. Ferrara, A. Marrani, On the moduli space of non-BPS attractors for N = 2 symmetric manifolds. Phys. Lett. B652, 111 (2007). arXiV:0706.1667

    Google Scholar 

  63. A. Ceresole, S. Ferrara, A. Marrani, 4d /5d correspondence for the black hole potential and its critical points. Class. Quant. Grav. 24, 5651 (2007). arXiV:0707.0964

    Google Scholar 

  64. L. Andrianopoli, R. D’Auria, S. Ferrara, M. Trigiante, Fake superpotential for large and small extremal black holes. JHEP 1008, 126 (2010). arXiv:1002.4340

    Google Scholar 

  65. F. Larsen, The attractor mechanism in five dimensions. Lect. Notes Phys. 755, 249 (2008). hep-th/0608191

    Google Scholar 

  66. L. Andrianopoli, S. Ferrara, A. Marrani, M. Trigiante, Non-BPS attractors in 5d and 6d extended supergravity. Nucl. Phys. B795, 428 (2008). arXiv:0709.3488

    Google Scholar 

  67. S. Ferrara, A. Marrani, J.F. Morales, H. Samtleben, Intersecting attractors. Phys. Rev. D79, 065031 (2009). arXiv:0812.0050

    Google Scholar 

  68. B.L. Cerchiai, S. Ferrara, A. Marrani, B. Zumino, Charge orbits of extremal black holes in five dimensional supergravity. Phys. Rev. D82, 085010 (2010). arXiv:1006.3101

    Google Scholar 

  69. E.G. Gimon, F. Larsen, J. Simon, Black holes in supergravity: The non-BPS branch. JHEP 0801, 040 (2008). arXiv:0710.4967

    Google Scholar 

  70. S. Bellucci, S. Ferrara, A. Marrani, A. Yeranyan, stu Black holes unveiled. Entropy 10(4), 507 (2008). arXiv:0807.3503

    Google Scholar 

  71. B.L. Cerchiai, S. Ferrara, A. Marrani, B. Zumino, Duality, entropy and ADM mass in supergravity. Phys. Rev. D79, 125010 (2009). arXiv:0902.3973

    Google Scholar 

  72. L. Borsten, D. Dahanayake, M.J. Duff, S. Ferrara, A. Marrani, W. Rubens. Observations on integral and continuous U -duality orbits in N= 8 supergravity. Class. Quant. Grav. 27, 185003 (2010). arXiv:1002.4223

    Google Scholar 

  73. P.K. Tripathy, S.P. Trivedi, Non-supersymmetric attractors in string theory. JHEP 0603, 022 (2006). hep-th/0511117

    Google Scholar 

  74. P.K. Tripathy, S.P. Trivedi, On the stability of non-supersymmetric attractors in string theory. JHEP 0708, 054 (2007). arXiv:0705.4554

    Google Scholar 

  75. L. Andrianopoli, R. D’Auria, S. Ferrara, Supersymmetry reduction of N extended supergravities in four dimensions. JHEP0203, 025 (2002). hep-th/0110277

    Google Scholar 

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Acknowledgements

The contents of this brief report result from collaborations with Stefano Bellucci, Murat Günaydin, Renata Kallosh, and especially Sergio Ferrara, which are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Physics, Theory Unit, CERN, 1211, Geneva 23, Switzerland

    Alessio Marrani

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  1. Alessio Marrani
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Correspondence to Alessio Marrani .

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Editors and Affiliations

  1. Dépt. Physique, Div. Théorie, CERN, Genève, 1211, Switzerland

    Sergio Ferrara

  2. Department of Mathematics, University of Bologna, Piazza Porta San Donato 5, Bologna, 40126, Italy

    Rita Fioresi

  3. Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, 90095, California, USA

    V.S. Varadarajan

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Marrani, A. (2011). Charge Orbits and Moduli Spaces of Black Hole Attractors. In: Ferrara, S., Fioresi, R., Varadarajan, V. (eds) Supersymmetry in Mathematics and Physics. Lecture Notes in Mathematics(), vol 2027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21744-9_8

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