Abstract
We point out that unitary representations of the Virasoro algebra contain Berry phases obtained by acting on a primary state with conformal transformations that trace a closed path on a Virasoro coadjoint orbit. These phases can be computed exactly thanks to the Maurer-Cartan form on the Virasoro group, and they persist after combining left- and right-moving sectors. Thinking of Virasoro representations as particles in AdS3 dressed with boundary gravitons, the Berry phases associated with Brown-Henneaux diffeomorphisms provide a gravitational extension of Thomas precession.
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Oblak, B. Berry phases on Virasoro orbits. J. High Energ. Phys. 2017, 114 (2017). https://doi.org/10.1007/JHEP10(2017)114
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DOI: https://doi.org/10.1007/JHEP10(2017)114