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Index theory and dynamical symmetry enhancement of M-horizons

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Abstract

We show that near-horizon geometries of 11-dimensional supergravity preserve an even number of supersymmetries. The proof follows from Lichnerowicz type theorems for two horizon Dirac operators, the field equations and Bianchi identities, and the vanishing of the index of a Dirac operator on the 9-dimensional horizon sections. As a consequence of this, we also prove that all M-horizons with non-vanishing fluxes admit a \( sl\left( {2,\mathbb{R}} \right) \) subalgebra of symmetries.

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References

  1. G. Gibbons and P. Townsend, Vacuum interpolation in supergravity via super p-branes, Phys. Rev. Lett. 71 (1993) 3754 [hep-th/9307049] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. J. Isenberg and V. Moncrief, Symmetries of cosmological Cauchy horizons, Commun. Math. Phys. 89 (1983) 387.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. H. Friedrich, I. Racz and R.M. Wald, On the rigidity theorem for space-times with a stationary event horizon or a compact Cauchy horizon, Commun. Math. Phys. 204 (1999) 691 [gr-qc/9811021] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. J. Gutowski and G. Papadopoulos, Static M-horizons, JHEP 01 (2012) 005 [arXiv:1106.3085] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. J. Gutowski and G. Papadopoulos, M-horizons, JHEP 12 (2012) 100 [arXiv:1207.7086] [INSPIRE].

    Article  ADS  Google Scholar 

  6. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. W. Israel, Event horizons in static vacuum space-times, Phys. Rev. 164 (1967) 1776 [INSPIRE].

    Article  ADS  Google Scholar 

  8. B. Carter, Axisymmetric black hole has only two degrees of freedom, Phys. Rev. Lett. 26 (1971) 331 [INSPIRE].

    Article  ADS  Google Scholar 

  9. S. Hawking, Black holes in general relativity, Commun. Math. Phys. 25 (1972) 152 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. D. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975) 905 [INSPIRE].

    Article  ADS  Google Scholar 

  11. W. Israel, Event horizons in static electrovac space-times, Commun. Math. Phys. 8 (1968) 245 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. P. Mazur, Proof of uniqueness of the Kerr-Newman black hole solution, J. Phys. A 15 (1982) 3173 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. D. Robinson, Four decades of black hole uniqueness theorems, in The Kerr spacetime: rotating black holes in general relativity, D.L. Wiltshire et al. eds., Cambridge University Press, Cambridge U.K. (2009).

  14. G.W. Gibbons, D. Ida and T. Shiromizu, Uniqueness and nonuniqueness of static black holes in higher dimensions, Phys. Rev. Lett. 89 (2002) 041101 [hep-th/0206049] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. M. Rogatko, Uniqueness theorem of static degenerate and nondegenerate charged black holes in higher dimensions, Phys. Rev. D 67 (2003) 084025 [hep-th/0302091] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  16. M. Rogatko, Classification of static charged black holes in higher dimensions, Phys. Rev. D 73 (2006) 124027 [hep-th/0606116] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. P. Figueras and J. Lucietti, On the uniqueness of extremal vacuum black holes, Class. Quant. Grav. 27 (2010) 095001 [arXiv:0906.5565] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, World-volume effective theory for higher-dimensional black holes, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of blackfold dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. H.S. Reall, Higher dimensional black holes and supersymmetry, Phys. Rev. D 68 (2003) 024024 [Erratum ibid. D 70 (2004) 089902] [hep-th/0211290] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  21. H. Elvang, R. Emparan, D. Mateos and H.S. Reall, A supersymmetric black ring, Phys. Rev. Lett. 93 (2004) 211302 [hep-th/0407065] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. J. Gutowski and G. Papadopoulos, Topology of supersymmetric N = 1, D = 4 supergravity horizons, JHEP 11 (2010) 114 [arXiv:1006.4369] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. N. Kim and J.-D. Park, Comments on AdS 2 solutions of D = 11 supergravity, JHEP 09 (2006) 041 [hep-th/0607093] [INSPIRE].

    Article  ADS  Google Scholar 

  24. J. Grover, J. Gutowski, G. Papadopoulos and W. Sabra, Index theory and supersymmetry of 5D horizons, arXiv:1303.0853 [INSPIRE].

  25. U. Gran, G. Papadopoulos and D. Roest, Systematics of M-theory spinorial geometry, Class. Quant. Grav. 22 (2005) 2701 [hep-th/0503046] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. E. Cremmer, B. Julia and J. Scherk, Supergravity theory in eleven-dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].

    ADS  Google Scholar 

  27. M.F. Atiyah and I.M. Singer, The Index of elliptic operators. 1, Annals Math. 87 (1968) 484.

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Gutowski and G. Papadopoulos, Heterotic black horizons, JHEP 07 (2010) 011 [arXiv:0912.3472] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. J. Gutowski and G. Papadopoulos, Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces, JHEP 10 (2010) 084 [arXiv:1003.2864] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. M. Akyol and G. Papadopoulos, Topology and geometry of 6-dimensional (1, 0) supergravity black hole horizons, Class. Quant. Grav. 29 (2012) 055002 [arXiv:1109.4254] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. U. Gran, J. Gutowski and G. Papadopoulos, IIB black hole horizons with five-form flux and KT geometry, JHEP 05 (2011) 050 [arXiv:1101.1247] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. U. Gran, J. Gutowski and G. Papadopoulos, IIB black hole horizons with five-form flux and extended supersymmetry, JHEP 09 (2011) 047 [arXiv:1104.2908] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Surrey, Guildford, GU2 7XH, U.K.

    J. Gutowski

  2. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, U.K.

    G. Papadopoulos

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  1. J. Gutowski
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  2. G. Papadopoulos
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Correspondence to J. Gutowski.

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Gutowski, J., Papadopoulos, G. Index theory and dynamical symmetry enhancement of M-horizons. J. High Energ. Phys. 2013, 88 (2013). https://doi.org/10.1007/JHEP05(2013)088

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