  We consider theoretically one-dimensional polariton ring accounting for both
longitudinal-transverse (TE-TM) and Zeeman splitting of spinor polariton states
and spin dependent polariton-polariton interactions. We present the novel class
of solutions in the form of the localized defects rotating with constant
angular velocity and analyze their properties for realistic values of the
parameters of the system. We show that the effects of the geometric phase
arising from the interplay between external magnetic field and TE-TM splitting
introduce chirality in the system and make solitons propagating in clockwise
and anticlockwise directions non equivalent. This can be interpreted as
solitonic analog of Aharonov-Bohm effect.
