Abstract
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 \( \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{R}}\right)/\mathrm{U}(1) \) 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.
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Giribet, G. Stringy horizons and generalized FZZ duality in perturbation theory. J. High Energ. Phys. 2017, 69 (2017). https://doi.org/10.1007/JHEP02(2017)069
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DOI: https://doi.org/10.1007/JHEP02(2017)069