Black hole entropy reveals a twelfth dimension

Itzhak Bars

doi:10.1103/PhysRevD.55.3633

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Black hole entropy reveals a twelfth dimension

Itzhak Bars

TH Division, CERN, CH-1211 Geneva 23, Switzerland

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Phys. Rev. D 55, 3633 – Published 15 March, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.3633

Abstract

The Bekenstein-Hawking black hole entropy in string theory and its generalizations, as expressed in terms of charges that correspond to central extensions of the supersymmetry algebra, has more symmetries than $U$ duality. It is invariant under transformations of the charges, involving a twelfth (or thirteenth) “dimension.” This is an indication that the secret theory behind string theory has a superalgebra involving Lorentz nonscalar extensions (that are not strictly central), as suggested in $S$ theory, and which could be hidden in $M$ or $F$ theories. It is suggested that the idea of spacetime is broader than usual, and that a larger “spacetime” is partially present in black holes.

References (24)

A. Strominger and C. Vafa, Phys. Lett. B379, 104 (1996); J. Breckenridge, D. Lowe, R. Myers, A. Peet, A. Strominger, and C. Vafa, 381, 423 (1996).
G. Horowitz and A. Strominger, Phys. Rev. Lett.77, 2363 (1996); G. Horowitz, J. Maldacena, and A. Strominger, Phys. Lett. B383, 151 (1996).
G. Horowitz, “The origin of black hole entropy in string theory,” Report No. gr-qc/9604051 (unpublished).
M. Cvetic and D. Youm, Phys. Rev. D54, 2612 (1996); Nucl. Phys.B477, 449 (1996); B476, 118 (1996).
M. Cvetic and A. A. Tseytlin, Phys. Lett. B366, 95 (1996); Phys. Rev. D53, 5619 (1996).
E. Halyo, B. Kol, A. Rajaraman, and L. Susskind, “Counting Schwarzchild and charged black holes,” Report No. hep-th/9609075 (unpublished).
R. Dijkgraaf, E. Verlinde, and H. Verlinde, “BPS spectrum of the five brane and black hole entropy,” Report No. hep-th/9603126 (unpublished); “BPS quantization of the five brane,” Report No. hep-th/9604055 (unpublished).
R. Kallosh and B. Kol, Phys. Rev. D53, 5344 (1996).
S. Ferrara and R. Kallosh, Phys. Rev. D54, 1514 (1996); 54, 1525 (1996).
M. Cvetic and C. Hull, Nucl. Phys.B480, 296 (1996).
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova, and W. Kai Wong, Phys. Rev. D54, 6293 (1996).
R. Kallosh and A. Rajaraman, Phys. Rev. D54, 6381 (1996).
J. Polchinski, Phys. Rev. Lett.75, 4724 (1995); See also J. Polchinski, S. Chaudhuri, and C. V. Johnson, “Notes on D-branes,” Report No. hep-th/9602052 (unpublished).
C. Hull and P. Townsend, Nucl. Phys.B438, 109 (1995).
I. Bars, Phys. Rev. D54, 5203 (1996); in Proceedings of Frontiers in Quantum Field Theory, Toyonaka, Japan, 1996 (unpublished), Report No. hep-th/9604200 (unpublished).
I. Bars, Phys. Rev. D55, 2373 (1997).
E. Witten, Nucl. Phys.B443, 85 (1995); “Some comments on String Dynamics,” Report No. hep-th/9507121, in the Proceedings of Strings ’95 (in press); P. Horava and E. Witten, Nucl. Phys.B460, 506 (1996).
P. Townsend, “p-brane democracy,” Report No. hep-th/9507048 (unpublished).
J. Schwarz, Phys. Lett. B367, 97 (1996); in Theory of Elementary Particles, Proceedings of the 29th International Ahrenshoop Symposium, Buckow, Germany, 1995, edited by D. Lust and G. Weigt [Nucl. Phys. B (Proc. Suppl.) 49 (1996)]; Report No. hep-th/9509148 (unpublished), “M-theory extensions of T duality,” Report No. hep-th/9601077 (unpublished).
C. Vafa, Nucl. Phys.B469, 403 (1996); D. R. Morrison and C. Vafa, B473, 74 (1996); B476, 437 (1996); E. Witten, B471, 195 (1996).
I. Bars, Phys. Rev. D52, 3567 (1995); I. Bars and S. Yankielowicz, 53, 4489 (1996); I. Bars, in Theory of Elementary Particles [19], p. 115.
E. Cremmer, “On hidden symmetries in extended supergravities, ” Report No. LPTENS 83/1, 1983 (unpublished); presented at the September School on Supergravity and Supersymmetry, Trieste, Italy, 1982, Trieste Workshop 1982, Report No. QC178:T7:1982 (unpublished), p. 153.
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E. Martinec, “Geometrical structures of M-theory,” Report No. hep-th/9608017 (unpublished).

[c1] A. Strominger and C. Vafa, Phys. Lett. B379, 104 (1996); J. Breckenridge, D. Lowe, R. Myers, A. Peet, A. Strominger, and C. Vafa, 381, 423 (1996).

[c2] G. Horowitz and A. Strominger, Phys. Rev. Lett.77, 2363 (1996); G. Horowitz, J. Maldacena, and A. Strominger, Phys. Lett. B383, 151 (1996).

[c3] G. Horowitz, “The origin of black hole entropy in string theory,” Report No. gr-qc/9604051 (unpublished).

[c4] M. Cvetic and D. Youm, Phys. Rev. D54, 2612 (1996); Nucl. Phys.B477, 449 (1996); B476, 118 (1996).

[c5] M. Cvetic and A. A. Tseytlin, Phys. Lett. B366, 95 (1996); Phys. Rev. D53, 5619 (1996).

[c6] E. Halyo, B. Kol, A. Rajaraman, and L. Susskind, “Counting Schwarzchild and charged black holes,” Report No. hep-th/9609075 (unpublished).

[c7] R. Dijkgraaf, E. Verlinde, and H. Verlinde, “BPS spectrum of the five brane and black hole entropy,” Report No. hep-th/9603126 (unpublished); “BPS quantization of the five brane,” Report No. hep-th/9604055 (unpublished).

[c8] R. Kallosh and B. Kol, Phys. Rev. D53, 5344 (1996).

[c9] S. Ferrara and R. Kallosh, Phys. Rev. D54, 1514 (1996); 54, 1525 (1996).

[c10] M. Cvetic and C. Hull, Nucl. Phys.B480, 296 (1996).

[c11] K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova, and W. Kai Wong, Phys. Rev. D54, 6293 (1996).

[c12] R. Kallosh and A. Rajaraman, Phys. Rev. D54, 6381 (1996).

[c13] J. Polchinski, Phys. Rev. Lett.75, 4724 (1995); See also J. Polchinski, S. Chaudhuri, and C. V. Johnson, “Notes on D-branes,” Report No. hep-th/9602052 (unpublished).

[c14] C. Hull and P. Townsend, Nucl. Phys.B438, 109 (1995).

[c15] I. Bars, Phys. Rev. D54, 5203 (1996); in Proceedings of Frontiers in Quantum Field Theory, Toyonaka, Japan, 1996 (unpublished), Report No. hep-th/9604200 (unpublished).

[c16] I. Bars, Phys. Rev. D55, 2373 (1997).

[c17] E. Witten, Nucl. Phys.B443, 85 (1995); “Some comments on String Dynamics,” Report No. hep-th/9507121, in the Proceedings of Strings ’95 (in press); P. Horava and E. Witten, Nucl. Phys.B460, 506 (1996).

[c18] P. Townsend, “p-brane democracy,” Report No. hep-th/9507048 (unpublished).

[c19] J. Schwarz, Phys. Lett. B367, 97 (1996); in Theory of Elementary Particles, Proceedings of the 29th International Ahrenshoop Symposium, Buckow, Germany, 1995, edited by D. Lust and G. Weigt [Nucl. Phys. B (Proc. Suppl.) 49 (1996)]; Report No. hep-th/9509148 (unpublished), “M-theory extensions of T duality,” Report No. hep-th/9601077 (unpublished).

[c20] C. Vafa, Nucl. Phys.B469, 403 (1996); D. R. Morrison and C. Vafa, B473, 74 (1996); B476, 437 (1996); E. Witten, B471, 195 (1996).

[c21] I. Bars, Phys. Rev. D52, 3567 (1995); I. Bars and S. Yankielowicz, 53, 4489 (1996); I. Bars, in Theory of Elementary Particles [19], p. 115.

[c22] E. Cremmer, “On hidden symmetries in extended supergravities, ” Report No. LPTENS 83/1, 1983 (unpublished); presented at the September School on Supergravity and Supersymmetry, Trieste, Italy, 1982, Trieste Workshop 1982, Report No. QC178:T7:1982 (unpublished), p. 153.

[c23] H. Nishino and E. Sezgin, Phys. Lett. B388, 569 (1996).

[c24] E. Martinec, “Geometrical structures of M-theory,” Report No. hep-th/9608017 (unpublished).

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