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We investigate finite $\alpha '$ effects in string theory on a black holebackground. By explicitly computing tree level scattering amplitudes, weconfirm a duality between seemingly different states recently conjectured byGiveon, Itzhaki, and Kutasov in [arXiv:1603.05822]. We verify that the relevant3-point functions factorize in such a way that the duality between oscillatorand winding states becomes manifest. This leads to determine the precisenormalization of the dual vertex operators, and confirms at the level of theinteracting theory the identification of states suggested by the analysis ofthe spectrum. This result implies a duality between two seemingly distinctmechanisms driving the violation of the string winding number in the black holeatmosphere.

Scattering of low lying states in the black hole atmosphere