Abstract
We investigate various geometrical aspects of the notion of ‘optical depth’ in the thermal atmosphere of black hole horizons. Optical depth has been proposed as a measure of fast-crambling times in such black hole systems, and the associated optical metric suggests that classical chaos plays a leading role in the actual scrambling mechanism. We study the behavior of theoptical depth with the size of the system and find that AdS/CFT phase transitions with topology change occur naturally as the scrambler becomes smaller than its thermal length. In the context of detailed AdS/CFT models basedon D-branes, T-duality implies that small scramblers are described in terms of matrix quantum mechanics.
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References
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [SPIRES].
Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [SPIRES].
L. Susskind, Addendum to fast scramblers, arXiv:1101.6048 [SPIRES].
J.L.F. Barbon and J.M. Magan, Chaotic fast scrambling at black holes, arXiv:1105.2581 [SPIRES].
G.W. Gibbons and M.J. Perry, Black holes and thermal green’s functions, Proc. Roy. Soc. Lond. A 358 (1978) 467 [SPIRES].
G. Kennedy, R. Critchley and J.S. Dowker, Finite temperature field theory with boundaries: stress tensor and surface action renormalization, Ann. Phys. 125 (1980) 346 [SPIRES].
J.L.F. Barbon, Horizon divergences of fields and strings in black hole backgrounds, Phys. Rev. D 50 (1994) 2712 [hep-th/9402004] [SPIRES].
I. Sachs and S.N. Solodukhin, Horizon holography, Phys. Rev. D 64 (2001) 124023 [hep-th/0107173] [SPIRES].
S.N. Solodukhin, Entanglement entropy of black holes, arXiv:1104.3712 [SPIRES].
G.W. Gibbons and C.M. Warnick, Universal properties of the near-horizon optical geometry, Phys. Rev. D 79 (2009) 064031 [arXiv:0809.1571] [SPIRES].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [SPIRES].
T. Damour, Black hole eddy currents, Phys. Rev. D 18 (1978) 3598 [SPIRES].
K.S..Thorne, R.H..Price and D.A..Macdonald, Black holes: the membrane paradigm, Yale University Press, U.S.A. (1986).
L. Susskind and J. Lindesay, An introduction to black holes, information and the string theory revolution: The holographic universe, World Scientific, Singapore (2005).
J.L.F. Barbon and E. Rabinovici, Extensivity versus holography in Anti-de Sitter spaces, Nucl. Phys. B 545 (1999) 371 [hep-th/9805143] [SPIRES].
J.L.F. Barbon, I.I. Kogan and E. Rabinovici, On stringy thresholds in SYM/AdS thermodynamics, Nucl. Phys. B 544 (1999) 104 [hep-th/9809033] [SPIRES].
J.L.F. Barbon and E. Rabinovici, On 1/N corrections to the entropy of noncommutative Yang-Mills theories, JHEP 12 (1999) 017 [hep-th/9910019] [SPIRES].
J.L.F. Barbon, C.A. Fuertes and E. Rabinovici, Deconstructing the little Hagedorn holography, JHEP 09 (2007) 055 [arXiv:0707.1158] [SPIRES].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [SPIRES].
R. Gregory and R. Laflamme, The instability of charged black strings and p-branes, Nucl. Phys. B 428 (1994) 399 [hep-th/9404071] [SPIRES].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [SPIRES].
G. Festuccia and H. Liu, The arrow of time, black holes and quantum mixing of large-N Yang-Mills theories, JHEP 12 (2007) 027 [hep-th/0611098] [SPIRES].
N. Iizuka and J. Polchinski, A matrix model for black hole thermalization, JHEP 10 (2008) 028 [arXiv:0801.3657] [SPIRES].
N. Iizuka, T. Okuda and J. Polchinski, Matrix models for the black hole information paradox, JHEP 02 (2010) 073 [arXiv:0808.0530] [SPIRES].
C. Asplund, D. Berenstein and D. Trancanelli, Evidence for fast thermalization in the BMN matrix model, arXiv:1104.5469 [SPIRES].
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ArXiv ePrint: 1106.4786
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Barbón, J.L.F., Magán, J.M. Fast scramblers of small size. J. High Energ. Phys. 2011, 35 (2011). https://doi.org/10.1007/JHEP10(2011)035
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DOI: https://doi.org/10.1007/JHEP10(2011)035