  We report the observation of vorticity in a macroscopic Bose-Einstein
condensate of polaritons in a ring geometry. Because it is a spinor condensate,
the elementary excitations are "half vortices" in which there is a phase
rotation of $\pi$ in connection with a polarization vector rotation of $\pi$
around a closed path. This is clearly seen in the experimental observations of
the polarization rotation around the ring. In the ring geometry, a new type of
half vortex is allowed in which the handedness of the spin flips from one side
of the ring to the other, in addition to the rotation of the linear
polarization component; such a state is not allowed in a simply-connected
geometry. Theoretical calculation of the energy of this state shows that when
many-body interactions are taken into account, it is lower in energy than a
simple half vortex. The direction of circulation of the flow around the ring
fluctuates randomly between clockwise and counterclockwise from one shot to the
next; this corresponds to spontaneous breaking of time-reversal symmetry in the
system. These new, macroscopic polariton ring condensates allow for the
possibility of direct control of the vorticity of the condensate.
