Abstract
It is well known that non-perturbative α′ corrections to the SL(2, ℝ)/U(1) cigar geometry are described via a condensation of a Sine-Liouville operator that schematically can be written as W + + W −, where W ± describe a string with winding number ±1. This condensation leads to interesting effects in the cigar geometry that take place already at the classical level in string theory. Condensation of the analytically continued Sine-Liouville operator in the Lorentzian SL(2, ℝ)/U(1) black hole is problematic. Here, we propose that in the black hole case, the non-perturbative α′ corrections are described in terms of an operator that can be viewed as the analytic continuation of the fusion of W + and W −. We show that this operator does not suffer from the same problem as the analytically continued Sine-Liouville operator and argue that it describes folded strings that fill the entire black hole and, in a sense, replace the black hole interior. We estimate the folded strings radiation, and show that they radiate at the Hawking temperature.
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References
I. Bars and D. Nemeschansky, String propagation in backgrounds with curved space-time, Nucl. Phys. B 348 (1991) 89 [INSPIRE].
S. Elitzur, A. Forge and E. Rabinovici, Some global aspects of string compactifications, Nucl. Phys. B 359 (1991) 581 [INSPIRE].
G. Mandal, A.M. Sengupta and S.R. Wadia, Classical solutions of two-dimensional string theory, Mod. Phys. Lett. A 6 (1991) 1685 [INSPIRE].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
R. Dijkgraaf, H.L. Verlinde and E.P. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371 (1992) 269 [INSPIRE].
V.A. Fateev, A.B. Zamolodchikov and Al.B. Zamolodchikov, unpublished.
V. Kazakov, I.K. Kostov and D. Kutasov, A matrix model for the two-dimensional black hole, Nucl. Phys. B 622 (2002) 141 [hep-th/0101011] [INSPIRE].
A. Giveon and D. Kutasov, Notes on AdS3 , Nucl. Phys. B 621 (2002) 303 [hep-th/0106004] [INSPIRE].
O. Aharony, A. Giveon and D. Kutasov, LSZ in LST, Nucl. Phys. B 691 (2004) 3 [hep-th/0404016] [INSPIRE].
J.L. Karczmarek, J.M. Maldacena and A. Strominger, Black hole non-formation in the matrix model, JHEP 01 (2006) 039 [hep-th/0411174] [INSPIRE].
A. Giveon, D. Kutasov, E. Rabinovici and A. Sever, Phases of quantum gravity in AdS3 and linear dilaton backgrounds, Nucl. Phys. B 719 (2005) 3 [hep-th/0503121] [INSPIRE].
D. Kutasov, Accelerating branes and the string/black hole transition, hep-th/0509170 [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, Stringy horizons, JHEP 06 (2015) 064 [arXiv:1502.03633] [INSPIRE].
R. Ben-Israel, A. Giveon, N. Itzhaki and L. Liram, Stringy horizons and UV/IR mixing, JHEP 11 (2015) 164 [arXiv:1506.07323] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, Stringy horizons II, JHEP 10 (2016) 157 [arXiv:1603.05822] [INSPIRE].
J.M. Maldacena and A. Strominger, Semiclassical decay of near extremal five-branes, JHEP 12 (1997) 008 [hep-th/9710014] [INSPIRE].
N. Itzhaki, Stringy instability inside the black hole, JHEP 10 (2018) 145 [arXiv:1808.02259] [INSPIRE].
I. Bars and J. Schulze, Folded strings falling into a black hole, Phys. Rev. D 51 (1995) 1854 [hep-th/9405156] [INSPIRE].
I. Bars, Folded strings in curved space-time, hep-th/9411078 [INSPIRE].
I. Bars, Folded strings, hep-th/9412044 [INSPIRE].
M. Bershadsky and H. Ooguri, Hidden SL(n) symmetry in conformal field theories, Commun. Math. Phys. 126 (1989) 49 [INSPIRE].
A. Gerasimov et al., Wess-Zumino-Witten model as a theory of free fields, Int. J. Mod. Phys. A 5 (1990) 2495 [INSPIRE].
G. Giribet and C.A. Núñez, Aspects of the free field description of string theory on AdS3, JHEP 06 (2000) 033 [hep-th/0006070] [INSPIRE].
G. Giribet and C.A. Núñez, Correlators in AdS3 string theory, JHEP 06 (2001) 010 [hep-th/0105200] [INSPIRE].
M. Wakimoto, Fock representations of the affine lie algebra A1 (1), Commun. Math. Phys. 104 (1986) 605 [INSPIRE].
T. Fukuda and K. Hosomichi, Three point functions in sine-Liouville theory, JHEP 09 (2001) 003 [hep-th/0105217] [INSPIRE].
J. Polchinski, String theory and black hole complementarity, hep-th/9507094 [INSPIRE].
M. Bershadsky and D. Kutasov, Comment on gauged WZW theory, Phys. Lett. B 266 (1991) 345 [INSPIRE].
D.J. Gross and P.F. Mende, The high-energy behavior of string scattering amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
D.J. Gross and P.F. Mende, String theory beyond the Planck scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
A. Giveon and N. Itzhaki, String theory at the tip of the cigar, JHEP 09 (2013) 079 [arXiv:1305.4799] [INSPIRE].
J.J. Atick and E. Witten, The Hagedorn Transition and the Number of Degrees of Freedom of String Theory, Nucl. Phys. B 310 (1988) 291 [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
A.M. Polyakov, Thermal properties of gauge fields and quark liberation, Phys. Lett. B 72 (1978) 477.
L. Susskind, Lattice models of quark confinement at high temperature, Phys. Rev. D 20 (1979) 2610 [INSPIRE].
O. Aharony and D. Kutasov, Holographic duals of long open strings, Phys. Rev. D 78 (2008) 026005 [arXiv:0803.3547] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave function of the universe, Phys. Rev. D 28 (1983) 2960 [Adv. Ser. Astrophys. Cosmol. 3 (1987) 174] [INSPIRE].
O. Aharony and E. Witten, Anti-de Sitter space and the center of the gauge group, JHEP 11 (1998) 018 [hep-th/9807205] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [hep-th/0111180] [INSPIRE].
J.M. Maldacena, Long strings in two dimensional string theory and non-singlets in the matrix model, JHEP 09 (2005) 078 [Int. J. Geom. Meth. Mod. Phys. 3 (2006) 1] [hep-th/0503112] [INSPIRE].
K. Attali and N. Itzhaki, The averaged null energy condition and the black hole interior in string theory, Nucl. Phys. B 943 (2019) 114631 [arXiv:1811.12117] [INSPIRE].
S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
J.M. Maldacena, Black holes in string theory, hep-th/9607235 [INSPIRE].
A.W. Peet, TASI lectures on black holes in string theory, hep-th/0008241 [INSPIRE].
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ArXiv ePrint: 1908.05000
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Giveon, A., Itzhaki, N. Stringy black hole interiors. J. High Energ. Phys. 2019, 14 (2019). https://doi.org/10.1007/JHEP11(2019)014
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DOI: https://doi.org/10.1007/JHEP11(2019)014