  We show theoretically that the strong coupling of circularly polarized
photons to an exciton in ring-like semiconductor nanostructures results in
physical nonequivalence of clockwise and counterclockwise exciton rotations in
the ring. As a consequence, the stationary energy splitting of exciton states
corresponding to these mutually opposite rotations appears. This excitonic
Aharonov-Bohm effect depends on the intensity and frequency of the circularly
polarized field and can be detected in state-of-the-art optical experiments.
