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We point out that unitary representations of the Virasoro algebra containBerry phases obtained by acting on a primary state with conformaltransformations that trace a closed path on a Virasoro coadjoint orbit. Thesephases can be computed exactly thanks to the Maurer-Cartan form on the Virasorogroup, and they persist after combining left- and right-moving sectors.Thinking of Virasoro representations as particles in AdS_3 dressed withboundary gravitons, the Berry phases associated with Brown-Henneauxdiffeomorphisms provide a gravitational extension of Thomas precession.

Berry Phases on Virasoro Orbits