Scattering of low lying states in the black hole atmosphere

We investigate finite $\alpha '$ effects in string theory on a black hole background. By explicitly computing tree level scattering amplitudes, we confirm a duality between seemingly different states recently conjectured by Giveon, Itzhaki, and Kutasov in [arXiv:1603.05822]. We verify that the relevant 3-point functions factorize in such a way that the duality between oscillator and winding states becomes manifest. This leads to determine the precise normalization of the dual vertex operators, and confirms at the level of the interacting theory the identification of states suggested by the analysis of the spectrum. This result implies a duality between two seemingly distinct mechanisms driving the violation of the string winding number in the black hole atmosphere.