  Magnetic field is a powerful tool for the manipulation of material's
electronic and optical properties. In the domain of transition metal
dichalcogenide monolayers, it allows one to unveil the spin, valley, and
orbital properties of many-body excitonic complexes. Here we study
theoretically the impact of normal-to-plane magnetic field on trions and
trion-polaritons. We demonstrate that spin and orbital effects of a magnetic
field give comparable contributions to the trion energies. Moreover, as
magnetic field redistributes the free electron gas between two valleys in the
conductance band, the trion-photon coupling becomes polarization and valley
dependent. This results in an effective giant Zeeman splitting of
trion-polaritons, in-line with the recent experimental observations.
