We study the duality between string theory formulated on a curved exact background (the two-dimensional black hole) and string theory in flat space with a tachyon-like potential. We generalize previous results on this subject by discussing a twisted version of the Fateev-Zamolodchikov-Zamolodchikov conjecture (FZZ). This duality is shown to hold at the level of N-point correlation functions on the sphere topology, and connects tree-level string amplitudes in the Euclidean version of the 2D black hole to correlation functions in a nonlinear sigma-model in flat space but in presence of a tachyon wall potential and a linear dilaton. The dual CFT we propose here corresponds to the perturbed 2D quantum gravity coupled to c < 1 matter, where the operator that describes the tachyon-like potential can be seen as an n = 2 momentum mode perturbation, while the usual sine-Liouville potential involved in the FZZ duality would correspond to the vortex sector n = 1. We give a precise prescription for computing correlation functions in the twisted model.
A twisted FZZ-like dual for the 2D black hole / G. Giribet, M. Leoni Olivera. - In: REPORTS ON MATHEMATICAL PHYSICS. - ISSN 0034-4877. - 61:2(2008 Apr), pp. 151-162. [10.1016/S0034-4877(08)00011-6]
A twisted FZZ-like dual for the 2D black hole
M. LEONI OLIVERAUltimo
2008
Abstract
We study the duality between string theory formulated on a curved exact background (the two-dimensional black hole) and string theory in flat space with a tachyon-like potential. We generalize previous results on this subject by discussing a twisted version of the Fateev-Zamolodchikov-Zamolodchikov conjecture (FZZ). This duality is shown to hold at the level of N-point correlation functions on the sphere topology, and connects tree-level string amplitudes in the Euclidean version of the 2D black hole to correlation functions in a nonlinear sigma-model in flat space but in presence of a tachyon wall potential and a linear dilaton. The dual CFT we propose here corresponds to the perturbed 2D quantum gravity coupled to c < 1 matter, where the operator that describes the tachyon-like potential can be seen as an n = 2 momentum mode perturbation, while the usual sine-Liouville potential involved in the FZZ duality would correspond to the vortex sector n = 1. We give a precise prescription for computing correlation functions in the twisted model.Pubblicazioni consigliate
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