Stringy horizons II. (English) Zbl 1390.83199
Summary: We show that the spectrum of normalizable states on a Euclidean \(\mathrm{SL}(2, \mathbb R)/\mathrm U(1)\) black hole exhibits a duality between oscillator states and wound strings. This duality generalizes the identification between a normalizable mode of dilaton gravity on the cigar and a mode of the tachyon with winding number one around the Euclidean time circle, which plays an important role in the FZZ correspondence. It implies that normalizable states on a large Euclidean black hole have support at widely separated scales. In particular, localized states that are extended over the cap of the cigar (the Euclidian analog of the black hole atmosphere) have a component that is localized near the tip of the cigar (the analog of the stretched horizon). As a consequence of this duality, the states exhibit a transition as a function of radial excitation level. From the perspective of a low energy probe, low lying states are naturally thought of as oscillator states in the black hole atmosphere, while at large excitation level they are naturally described as wound strings. As the excitation level increases, the size of the states first decreases and then increases. This behavior is expected to be a general feature of black hole horizons in string theory.
For part I, see [the authors, ibid. 2015, No. 6, Paper No. 64, 13 p. (2015; Zbl 1388.83447)].
For part I, see [the authors, ibid. 2015, No. 6, Paper No. 64, 13 p. (2015; Zbl 1388.83447)].
Citations:
Zbl 1388.83447References:
| [1] | Bekenstein, JD, Black holes and entropy, Phys. Rev., D 7, 2333, (1973) · Zbl 1369.83037 |
| [2] | S.W. Hawking, Particle creation by black holes, Commun. Math. Phys.43 (1975) 199 [Erratum ibid.46 (1976) 206] [INSPIRE]. · Zbl 1378.83040 |
| [3] | D. Kutasov, Accelerating branes and the string/black hole transition, hep-th/0509170 [INSPIRE]. |
| [4] | Barbon, JLF; Rabinovici, E., Remarks on black hole instabilities and closed string tachyons, Found. Phys., 33, 145, (2003) · doi:10.1023/A:1022823926674 |
| [5] | Elitzur, S.; Forge, A.; Rabinovici, E., Some global aspects of string compactifications, Nucl. Phys., B 359, 581, (1991) · doi:10.1016/0550-3213(91)90073-7 |
| [6] | Mandal, G.; Sengupta, AM; Wadia, SR, Classical solutions of two-dimensional string theory, Mod. Phys. Lett., A 6, 1685, (1991) · Zbl 1021.81757 · doi:10.1142/S0217732391001822 |
| [7] | Witten, E., On string theory and black holes, Phys. Rev., D 44, 314, (1991) · Zbl 0900.53037 |
| [8] | Dijkgraaf, R.; Verlinde, HL; Verlinde, EP, String propagation in a black hole geometry, Nucl. Phys., B 371, 269, (1992) · Zbl 0925.81230 · doi:10.1016/0550-3213(92)90237-6 |
| [9] | Giveon, A.; Itzhaki, N., String theory versus black hole complementarity, JHEP, 12, 094, (2012) · Zbl 1397.83147 · doi:10.1007/JHEP12(2012)094 |
| [10] | Giveon, A.; Itzhaki, N., String theory at the tip of the cigar, JHEP, 09, 079, (2013) · Zbl 1342.83370 · doi:10.1007/JHEP09(2013)079 |
| [11] | Mertens, TG; Verschelde, H.; Zakharov, VI, Near-Hagedorn thermodynamics and random walks: a general formalism in curved backgrounds, JHEP, 02, 127, (2014) · doi:10.1007/JHEP02(2014)127 |
| [12] | Mertens, TG; Verschelde, H.; Zakharov, VI, Random walks in Rindler spacetime and string theory at the tip of the cigar, JHEP, 03, 086, (2014) · doi:10.1007/JHEP03(2014)086 |
| [13] | Giveon, A.; Itzhaki, N.; Troost, J., The black hole interior and a curious sum rule, JHEP, 03, 063, (2014) · Zbl 1333.83077 · doi:10.1007/JHEP03(2014)063 |
| [14] | Giveon, A.; Itzhaki, N.; Troost, J., Lessons on black holes from the elliptic genus, JHEP, 04, 160, (2014) · Zbl 1333.83078 · doi:10.1007/JHEP04(2014)160 |
| [15] | Mertens, TG; Verschelde, H.; Zakharov, VI, the thermal scalar and random walks in AdS_{3}and BT Z, JHEP, 06, 156, (2014) · Zbl 1333.81296 · doi:10.1007/JHEP06(2014)156 |
| [16] | Mertens, TG; Verschelde, H.; Zakharov, VI, Near-Hagedorn thermodynamics and random walks — extensions and examples, JHEP, 11, 107, (2014) · doi:10.1007/JHEP11(2014)107 |
| [17] | Mertens, TG; Verschelde, H.; Zakharov, VI, On the relevance of the thermal scalar, JHEP, 11, 157, (2014) · doi:10.1007/JHEP11(2014)157 |
| [18] | Mertens, TG; Verschelde, H.; Zakharov, VI, Perturbative string thermodynamics near black hole horizons, JHEP, 06, 167, (2015) · doi:10.1007/JHEP06(2015)167 |
| [19] | Giveon, A.; Itzhaki, N.; Kutasov, D., Stringy horizons, JHEP, 06, 064, (2015) · Zbl 1388.83447 · doi:10.1007/JHEP06(2015)064 |
| [20] | Giribet, G.; Ranjbar, A., Screening stringy horizons, Eur. Phys. J., C 75, 490, (2015) · doi:10.1140/epjc/s10052-015-3714-0 |
| [21] | Mertens, TG; Verschelde, H.; Zakharov, VI, The long string at the stretched horizon and the entropy of large non-extremal black holes, JHEP, 02, 041, (2016) · Zbl 1388.83485 · doi:10.1007/JHEP02(2016)041 |
| [22] | Ben-Israel, R.; Giveon, A.; Itzhaki, N.; Liram, L., Stringy horizons and UV/IR mixing, JHEP, 11, 164, (2015) · Zbl 1387.83039 · doi:10.1007/JHEP11(2015)164 |
| [23] | T.G. Mertens, Hagedorn string thermodynamics in curved spacetimes and near black hole horizons, arXiv:1506.07798 [INSPIRE]. |
| [24] | J. Lin, Bulk locality from entanglement in gauge/gravity duality, arXiv:1510.02367 [INSPIRE]. |
| [25] | Ben-Israel, R.; Giveon, A.; Itzhaki, N.; Liram, L., On the stringy hartle-Hawking state, JHEP, 03, 019, (2016) · Zbl 1388.83386 · doi:10.1007/JHEP03(2016)019 |
| [26] | W. Cottrell and A. Hashimoto, Resolved gravity duals of N = 4 quiver field theories in 2 + 1 dimensions, arXiv:1602.04765 [INSPIRE]. · Zbl 1390.83099 |
| [27] | V.A. Fateev, A.B. Zamolodchikov and Al.B. Zamolodchikov, unpublished. |
| [28] | Kazakov, V.; Kostov, IK; Kutasov, D., A matrix model for the two-dimensional black hole, Nucl. Phys., B 622, 141, (2002) · Zbl 0988.81099 · doi:10.1016/S0550-3213(01)00606-X |
| [29] | Giveon, A.; Kutasov, D., Little string theory in a double scaling limit, JHEP, 10, 034, (1999) · Zbl 0957.81029 · doi:10.1088/1126-6708/1999/10/034 |
| [30] | Kazama, Y.; Suzuki, H., new N = 2 superconformal field theories and superstring compactification, Nucl. Phys., B 321, 232, (1989) · doi:10.1016/0550-3213(89)90250-2 |
| [31] | A. Giveon, N. Itzhaki and D. Kutasov, to appear. |
| [32] | Maldacena, JM; Ooguri, H., strings in AdS_{3}and SL(2, R) WZW model 1: the spectrum, J. Math. Phys., 42, 2929, (2001) · Zbl 1036.81033 · doi:10.1063/1.1377273 |
| [33] | Argurio, R.; Giveon, A.; Shomer, A., superstrings on AdS_{3}and symmetric products, JHEP, 12, 003, (2000) · Zbl 0990.81610 · doi:10.1088/1126-6708/2000/12/003 |
| [34] | Wakimoto, M., Fock representations of the affine Lie algebra \(A\)_{1}\^{}{(1)}, Commun. Math. Phys., 104, 605, (1986) · Zbl 0587.17009 · doi:10.1007/BF01211068 |
| [35] | Bernard, D.; Felder, G., Fock representations and BRST cohomology in SL(2) current algebra, Commun. Math. Phys., 127, 145, (1990) · Zbl 0703.17013 · doi:10.1007/BF02096498 |
| [36] | Bershadsky, M.; Kutasov, D., Comment on gauged WZW theory, Phys. Lett., B 266, 345, (1991) · doi:10.1016/0370-2693(91)91050-6 |
| [37] | Giveon, A.; Kutasov, D.; Seiberg, N., comments on string theory on AdS_{3}, Adv. Theor. Math. Phys., 2, 733, (1998) · Zbl 1041.81575 · doi:10.4310/ATMP.1998.v2.n4.a3 |
| [38] | J. Polchinski, String theory. Volume 2: superstring theory and beyond, section 10.4, Cambridge University Press, Cambridge U.K. (2005). · Zbl 1075.81053 |
| [39] | Horowitz, GT; Polchinski, J., A correspondence principle for black holes and strings, Phys. Rev., D 55, 6189, (1997) |
| [40] | Horowitz, GT; Polchinski, J., Selfgravitating fundamental strings, Phys. Rev., D 57, 2557, (1998) |
| [41] | Giveon, A.; Kutasov, D., Fundamental strings and black holes, JHEP, 01, 071, (2007) · doi:10.1088/1126-6708/2007/01/071 |
| [42] | Y. Sugawara, “Analytic continuation” of N = 2 minimal model, Prog. Theor. Exp. Phys.2014 (2014) 043B02 [arXiv:1311.4708] [INSPIRE]. · Zbl 1331.81203 |
| [43] | G. Giribet, Scattering of low lying states in the black hole atmosphere, Phys. Rev.D 94 (2016) 026008 [Addendum ibid.D 94 (2016) 049902] [arXiv:1606.06919] [INSPIRE]. |
| [44] | Mertens, TG; Verschelde, H.; Zakharov, VI, String theory in polar coordinates and the vanishing of the one-loop Rindler entropy, JHEP, 08, 113, (2016) · Zbl 1390.83349 · doi:10.1007/JHEP08(2016)113 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
