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This letter assigns the Faraday rotation in photoexcited semiconductors to``Pauli interactions'', \emph{i}. \emph{e}., carrier exchanges, between thereal excitons present in the sample and the virtual excitons coupled to the$\sigma_{\pm}$ parts of a linearly polarized light. While \emph{direct Coulomb}interactions scatter bright excitons into bright excitons, whatever their spinsare, \emph{Pauli} interactions do it for bright excitons \emph{with same spinonly}. This makes these Pauli interactions entirely responsible for therefractive index difference, which comes from processes in which the virtualexciton which is created and the one which recombines are formed with differentcarriers. To write this difference in terms of photon detuning and excitondensity, we use our new many-body theory for interacting excitons. Its multiarm``Shiva'' diagrams for $N$-body exchanges make transparent the physics involvedin the various terms. This work also shows the interesting link which existsbetween Faraday rotation and the exciton optical Stark effect

Faraday rotation in photoexcited semiconductors: A composite-exciton many-body effect