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Black holes and groups of type E 7

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Abstract

We report some results on the relation between extremal black holes in locally supersymmetric theories of gravity and groups of type E 7, appearing as generalized electric-magnetic duality symmetries in such theories. Some basics on the covariant approach to the stratification of the relevant symplectic representation are reviewed, along with a connection between special Kähler geometry and a ‘generalization’ of groups of type E 7.

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References

  1. R Arnowitt, S Deser and C W Misner, Phys. Rev. 117, 1595 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. S Ferrara, K Hayakawa and A Marrani, Fortsch. Phys. 56, 993 (2008), arXiv:0805.2498 [hep-th]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. S Ferrara, R Kallosh and A Strominger, Phys. Rev. D52, (1995) 5412 A Strominger, Phys. Lett. B383, 39 (1996) S Ferrara and R Kallosh, Phys. Rev. D54, 1514 (1996); Phys. Rev. D54, 1525 (1996)

  4. S Ferrara, G W Gibbons and R Kallosh, Nucl. Phys. B500, 75 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  5. L Andrianopoli, R D’Auria, S Ferrara and M Trigiante, Lect. Notes Phys. 737, 661 (2008), arXiv:hep-th/0611345

    Article  MathSciNet  ADS  Google Scholar 

  6. S Bellucci, S Ferrara, R Kallosh and A Marrani, Lect. Notes Phys. 755, 115 (2008), arXiv:0711.4547 [hep-th]

    MathSciNet  ADS  Google Scholar 

  7. S W Hawking, Phys. Rev. Lett. 26, 1344 (1971) J D Bekenstein, Phys. Rev. D7, 2333 (1973)

    Google Scholar 

  8. M K Gaillard and B Zumino, Nucl. Phys. B193, 221 (1981) P Aschieri, S Ferrara and B Zumino, Riv. Nuovo Cim. 31, 625 (2009), arXiv:0807.4039 [hep-th]

    Google Scholar 

  9. M J Duff, R R Khuri and J X Lu, Phys. Rep. 259, 213 (1995), arXiv:hep-th/9412184

    Article  MathSciNet  ADS  Google Scholar 

  10. G Gibbons and P K Townsend, Phys. Rev. Lett. 71, 3754 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. A Ceresole and G Dall’Agata, J. High Energy Phys. 0703, 110 (2007), arXiv:hep-th/0702088

    Article  MathSciNet  ADS  Google Scholar 

  12. S Ferrara and A Marrani, J. High Energy Phys. 1012, 038 (2010), arXiv:1009.3251 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  13. D Z Freedman, C Nunez, M Schnabl and K Skenderis, Phys. Rev. D69, 104027 (2004), arXiv:hep-th/0312055 A Celi, A Ceresole, G Dall’Agata, A Van Proeyen and M Zagermann, Phys. Rev. D71, 045009 (2005), arXiv:hep-th/0410126

  14. A Dabholkar, A Sen and S P Trivedi, J. High Energy Phys. 0701, 096 (2007), arXiv: hep-th/0611143

    Article  MathSciNet  ADS  Google Scholar 

  15. E G Gimon, F Larsen and J Simon, J. High Energy Phys. 0801, 040 (2008), arXiv: hep-th/0710.4967

    Article  MathSciNet  ADS  Google Scholar 

  16. L Andrianopoli, R D’Auria, E Orazi and M Trigiante, J. High Energy Phys. 0711, 032 (2007), arXiv:hep-th/0706.0712

    Article  MathSciNet  ADS  Google Scholar 

  17. G Lopes Cardoso, A Ceresole, G Dall’Agata, J M Oberreuter and J Perz, J. High Energy Phys. 0710, 063 (2007), arXiv:hep-th/0706.3373

    Google Scholar 

  18. S Bellucci, S Ferrara, A Marrani and A Yeranyan, stu black holes unveiled, arXiv:hep-th/ 0807.3503

  19. A Ceresole, G Dall’Agata, S Ferrara and A Yeranyan, Nucl. Phys. B824, 239 (2010), arXiv:0908.1110

    Article  MathSciNet  ADS  Google Scholar 

  20. A Ceresole, G Dall’Agata, S Ferrara and A Yeranyan, Nucl. Phys. B832, 358 (2010), arXiv:0910.2697

  21. G Bossard, Y Michel and B Pioline, Extremal black holes, nilpotent orbits and the true fake superpotential, arXiv:0908.1742

  22. S Ferrara, A Gnecchi and A Marrani, Phys. Rev. D78, 065003 (2008), arXiv:hep-th/0806. 3196 J Perz, P Smyth, T Van Riet and B Vercnocke, J. High Energy Phys. 0903, 150 (2009), arXiv:hep-th/0810.1528 K Goldstein and S Katmadas, J. High Energy Phys. 0905, 058 (2009), arXiv:hep-th/0812.4183 I Bena, G Dall’Agata, S Giusto, C Ruef and N P Warner, J. High Energy Phys. 0906, 015 (2009), arXiv:hep-th/0902.4526 P Galli and J Perz, Non-supersymmetric extremal multicenter black holes with superpotentials, arXiv:0909.5185

  23. L Andrianopoli, R D’Auria, E Orazi and M Trigiante, First order description of D=4 static black holes and the Hamilton–Jacobi equation, arXiv:hep-th/0905.3938

  24. M J Duff, J T Liu and J Rahmfeld, Nucl. Phys. B459, 125 (1996), arXiv:hep-th/9508094 K Behrndt, R Kallosh, J Rahmfeld, M Shmakova and W K Wong, Phys. Rev. D54, 6293 (1996), arXiv:hep-th/9608059

  25. A Strominger, Commun. Math. Phys. 133, 163 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. B de Wit, Introduction to black hole entropy and supersymmetry, hep-th/0503211

  27. R B Brown, J. Reine Angew. Math. 236, 79 (1969)

    MathSciNet  MATH  Google Scholar 

  28. E Cartan, \(\OE\) uvres complètes (Editions du Centre National de la Recherche Scientifique, Paris, 1984) E Cremmer and B Julia, Nucl. Phys. B159, 141 (1979)

  29. P Truini, Exceptional Lie algebras, SU(3) and Jordan pairs, arXiv:1112.1258 [math-ph]

  30. B Julia, Group disintegrations E Cremmer, Supergravities in 5 dimensions, in: Superspace and supergravity edited by S W Hawking and M Rocek (Cambridge Univ. Press, 1981)

    Google Scholar 

  31. S Ferrara and P Van Nieuwenhuizen, Phys. Rev. Lett. 17, 1669 (1976)

    Article  ADS  Google Scholar 

  32. S Ferrara, C Savoy and B Zumino, Nucl. Phys. B121, 393 (1977)

    Article  ADS  Google Scholar 

  33. L Borsten, D Dahanayake, M J Duff and W Rubens, Phys. Rev. D80, 026003 (2009), arXiv:0903.5517 [hep-th]

    MathSciNet  ADS  Google Scholar 

  34. S Ferrara, A Marrani and A Yeranyan, Phys. Lett. B701, 640 (2011), arXiv:1102.4857 [hep-th]

    MathSciNet  ADS  Google Scholar 

  35. R Kallosh and B Kol, Phys. Rev. D53, 5344 (1996), arXiv:hep-th/9602014

    MathSciNet  ADS  Google Scholar 

  36. M Gunaydin, G Sierra and P K Townsend, Phys. Lett. B133, 72 (1983)

    MathSciNet  ADS  Google Scholar 

  37. L Borsten, M J Duff, S Ferrara, A Marrani and W Rubens, Small Orbits, arXiv:1108.0424 [hep-th], to appear in Phys. Rev. D

  38. J C Ferrar, Trans. Amer. Math. Soc. 174, 313 (1972)

    Article  MathSciNet  Google Scholar 

  39. S Krutelevich, J. Algebra 314, 924 (2007), arXiv:math/0411104

    Article  MathSciNet  MATH  Google Scholar 

  40. S Ferrara and M Günaydin, Int. J. Mod. Phys. A13, 2075 (1998), hep-th/9708025

    ADS  Google Scholar 

  41. S Ferrara and J M Maldacena, Class. Quant. Grav. 15, 749 (1998), hep-th/9706097

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. R D’Auria, S Ferrara and M Lledó, Phys. Rev. D60, 084007 (1999), hep-th/9903089

    Google Scholar 

  43. R Slansky, Phys. Rep. 79, 1 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  44. O Shukuzawa, Commun. Algebra 34, 197 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  45. K Yokota, Exceptional Lie groups, arXiv:0902.0431 [math.DG]

  46. A Marrani, E Orazi and F Riccioni, J. Phys. A44, 155207 (2011), arXiv:1012.5797 [hep-th]

    MathSciNet  ADS  Google Scholar 

  47. A Galperin and O Ogievetsky, Phys. Lett. B301, 67 (1993), hep-th/9210153

    MathSciNet  ADS  Google Scholar 

  48. S Ferrara, A Marrani and A Yeranyan, On invariant structures of black hole charges, arXiv:1110.4004 [hep-th]

  49. S Ferrara, A Marrani and A Yeranyan, Phys. Lett. B701, 640 (2011), arXiv:1102.4857 [hep-th]

    MathSciNet  ADS  Google Scholar 

  50. B L Cerchiai, S Ferrara, A Marrani and B Zumino, Phys. Rev. D79, 125010 (2009), arXiv:0902.3973 [hep-th]

    MathSciNet  ADS  Google Scholar 

  51. A Ceresole, R D’Auria and S Ferrara, Nucl. Phys. Proc. Suppl. 46, 67 (1996), hep-th/9509160

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. L Andrianopoli, M Bertolini, A Ceresole, R D’Auria, S Ferrara, P Fré and T Magri, J. Geom. Phys. 23, 111 (1997), hep-th/9605032

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. L Castellani, R D’Auria and S Ferrara, Class. Quant. Grav. 7, 1767 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  54. L Castellani, R D’Auria and S Ferrara, Phys. Lett. B241, 57 (1990)

    MathSciNet  ADS  Google Scholar 

  55. B Craps, F Roose, W Troost and A Van Proeyen, Nucl. Phys. B503, 565 (1997), hep-th/ 9703082

    Article  ADS  Google Scholar 

  56. S Bellucci, A Marrani and R Roychowdhury, Int. J. Mod. Phys. A25, 1891 (2010), arXiv:0910.4249 [hep-th]

    MathSciNet  ADS  Google Scholar 

  57. S Bellucci, S Ferrara, R Kallosh and A Marrani, Lect. Notes Phys. 755, 115 (2008), arXiv.0711.4547 [hep-th]

    MathSciNet  ADS  Google Scholar 

  58. J F Luciani, Nucl. Phys. B132, 325 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  59. S Ferrara, A Gnecchi and A Marrani, Phys. Rev. D78, 065003 (2008), arXiv:0806.3196 [hep-th]

    MathSciNet  ADS  Google Scholar 

  60. S Ferrara, A Marrani and E Orazi, Nucl. Phys. B846, 512 (2011), arXiv:1010.2280 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  61. S Cecotti, S Ferrara and L Girardello, Int. J. Mod. Phys. A4, 2475 (1989)

    MathSciNet  ADS  Google Scholar 

  62. S Ferrara and S Sabharwal, Nucl. Phys. B332, 317 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  63. B de Wit, F Vanderseypen and A Van Proeyen, Nucl. Phys. B400, 463 (1993), hep-th/9210068

    Article  ADS  Google Scholar 

  64. J Bagger and E Witten, Nucl. Phys. B222, 1 (1983)

    Article  MathSciNet  ADS  Google Scholar 

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Correspondence to Sergio Ferrara.

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Ferrara, S., Marrani, A. Black holes and groups of type E 7 . Pramana - J Phys 78, 893–905 (2012). https://doi.org/10.1007/s12043-012-0315-4

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