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We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n − 2 winding modes actually coincide with the correlation functions in the SL(2ℝ)/U(1) gauged WZW model that include n − 2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference [1]. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature. © 2017, The Author(s).


Documento: Artículo
Título:Stringy horizons and generalized FZZ duality in perturbation theory
Autor:Giribet, G.
Filiación:Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, United States
Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Black Holes in String Theory; Bosonic Strings; Conformal Field Models in String Theory; Tachyon Condensation
Título revista:Journal of High Energy Physics
Título revista abreviado:J. High Energy Phys.


  • Giveon, A., Itzhaki, N., Kutasov, D., Stringy horizons II (2016) JHEP, 10, p. 157. , [arXiv:1603.05822] [INSPIRE]
  • V. Fateev, A. Zamolodchikov, and Al. Zamolodchikov, unpublished; Kazakov, V., Kostov, I.K., Kutasov, D., A matrix model for the two-dimensional black hole (2002) Nucl. Phys., B 622, p. 141. , [hep-th/0101011] [INSPIRE]
  • Hikida, Y., Schomerus, V., The FZZ-duality conjecture: a proof (2009) JHEP, 3, p. 095. , [arXiv:0805.3931] [INSPIRE]
  • Elitzur, S., Forge, A., Rabinovici, E., Some global aspects of string compactifications (1991) Nucl. Phys., B 359, p. 581. , [INSPIRE]
  • Mandal, G., Sengupta, A.M., Wadia, S.R., Classical solutions of two-dimensional string theory (1991) Mod. Phys. Lett., A 6, p. 1685. , [INSPIRE]
  • Witten, E., On string theory and black holes (1991) Phys. Rev., 500, p. 314. , [INSPIRE]
  • Giveon, A., Kutasov, D., Notes on AdS3 (2002) Nucl. Phys., B 621, p. 303. , [hep-th/0106004] [INSPIRE]
  • Hikida, Y., Takayanagi, T., On solvable time-dependent model and rolling closed string tachyon (2004) Phys. Rev., 500, p. 126013. , [hep-th/0408124] [INSPIRE]
  • Hori, K., Kapustin, A., Duality of the fermionic 2D black hole and N = 2 Liouville theory as mirror symmetry (2001) JHEP, 8, p. 045. , [hep-th/0104202] [INSPIRE]
  • Maldacena, J.M., Long strings in two dimensional string theory and non-singlets in the matrix model (2005) JHEP, 9, p. 078. , [hep-th/0503112] [INSPIRE]
  • Mukherjee, A., Mukhi, S., Pakman, A., FZZ algebra (2007) JHEP, 1, p. 025. , [hep-th/0606037] [INSPIRE]
  • Giribet, G., Scattering of low lying states in the black hole atmosphere (2016) Phys. Rev., 500, p. 026008. , [arXiv:1606.06919] [INSPIRE]
  • Giveon, A., Itzhaki, N., Kutasov, D., Stringy horizons (2015) JHEP, 6, p. 064. , [arXiv:1502.03633] [INSPIRE]
  • Giribet, G., Núñez, C.A., Correlators in AdS3 string theory (2001) JHEP, 6, p. 010. , [hep-th/0105200] [INSPIRE]
  • J.M. Maldacena and H. Ooguri, Strings in AdS 3 and the S L (2 ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006; Fukuda, T., Hosomichi, K., Three point functions in sine-Liouville theory (2001) JHEP, 9, p. 003. , [hep-th/0105217] [INSPIRE]
  • Dorn, H., Otto, H.J., Two and three point functions in Liouville theory (1994) Nucl. Phys., B 429, p. 375. , [hep-th/9403141] [INSPIRE]
  • Zamolodchikov, A.B., Zamolodchikov, A.B., Structure constants and conformal bootstrap in Liouville field theory (1996) Nucl. Phys., B 477, p. 577. , [hep-th/9506136] [INSPIRE]
  • Dotsenko, V.S., Fateev, V.A., Four point correlation functions and the operator algebra in the two-dimensional conformal invariant theories with the central charge c < 1 (1985) Nucl. Phys., B 251, p. 691. , [INSPIRE]
  • Baseilhac, P., Fateev, V.A., Expectation values of local fields for a two-parameter family of integrable models and related perturbed conformal field theories (1998) Nucl. Phys., B 532, p. 567. , [hep-th/9906010] [INSPIRE]
  • Fateev, V.A., Litvinov, A.V., Coulomb integrals in Liouville theory and Liouville gravity (2007) JETP Lett., 84, p. 531. , [INSPIRE]
  • Fateev, V.A., Litvinov, A.V., Multipoint correlation functions in Liouville field theory and minimal Liouville gravity (2008) Theor. Math. Phys., 154, p. 454. , [arXiv:0707.1664] [INSPIRE]
  • V. Fateev, privated communication; Giribet, G., The string theory on AdS3 as a marginal deformation of a linear dilaton background (2006) Nucl. Phys., B 737, p. 209. , [hep-th/0511252] [INSPIRE]
  • G. Giribet and M. Leoni, A twisted FZZ-like dual for the 2D black hole, Rept. Math. Phys. 61 (2008)151; Giribet, G., One-loop amplitudes of winding strings in AdS3 and the Coulomb gas approach (2016) Phys. Rev., 500, p. 064037. , [arXiv:1511.04017] [INSPIRE]
  • A.V. Stoyanovsky, A relation between the Knizhnik-Zamolodchikov and Belavin-Polyakov-Zamolodchikov systems of partial differential equations; Ribault, S., Teschner, J., H + (3)-WZNW correlators from Liouville theory (2005) JHEP, 6, p. 014. , [hep-th/0502048] [INSPIRE]
  • Hikida, Y., Schomerus, V., H+(3) WZNW model from Liouville field theory (2007) JHEP, 10, p. 064. , [arXiv:0706.1030] [INSPIRE]
  • Ribault, S., Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory (2005) JHEP, 9, p. 045. , [hep-th/0507114] [INSPIRE]
  • Goulian, M., Li, M., Correlation functions in Liouville theory (1991) Phys. Rev. Lett., 66, p. 2051. , [INSPIRE]
  • A.B. Zamolodchikov, Perturbed conformal field theory on fluctuating sphere; (2001), J.M. Maldacena and H. Ooguri, Strings in AdS 3 and S L (2 ℝ) WZW model 1. The spectrum, J. Math. Phys. 42 2929; Becker, K., Becker, M., Interactions in the SL(2ℝ)/U(1) black hole background (1994) Nucl. Phys., B 418, p. 206. , [hep-th/9310046] [INSPIRE]
  • Bershadsky, M., Kutasov, D., Comment on gauged WZW theory (1991) Phys. Lett., B 266, p. 345. , [INSPIRE]
  • Dijkgraaf, R., Verlinde, H.L., Verlinde, E.P., String propagation in a black hole geometry (1992) Nucl. Phys., B 371, p. 269. , [INSPIRE]
  • Giribet, G.E., Lopez-Fogliani, D.E., Remarks on free field realization of SL(2ℝ)(k)/U(1)×U(1) WZNW model (2004) JHEP, 6, p. 026. , [hep-th/0404231] [INSPIRE]


---------- APA ----------
(2017) . Stringy horizons and generalized FZZ duality in perturbation theory. Journal of High Energy Physics, 2017(2).
---------- CHICAGO ----------
Giribet, G. "Stringy horizons and generalized FZZ duality in perturbation theory" . Journal of High Energy Physics 2017, no. 2 (2017).
---------- MLA ----------
Giribet, G. "Stringy horizons and generalized FZZ duality in perturbation theory" . Journal of High Energy Physics, vol. 2017, no. 2, 2017.
---------- VANCOUVER ----------
Giribet, G. Stringy horizons and generalized FZZ duality in perturbation theory. J. High Energy Phys. 2017;2017(2).