Berry Phases on Virasoro Orbits

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 AdS_3 dressed with boundary gravitons, the Berry phases associated with Brown-Henneaux diffeomorphisms provide a gravitational extension of Thomas precession.Comment: 34 pages, 3 figures. v2: examples moved to appendix + minor clarifications. Published in JHE

Holographic positive energy theorems in three-dimensional gravity

The covariant phase space of three-dimensional asymptotically flat and anti-de Sitter gravity is controlled by well-understood coadjoint orbits of the Virasoro group. Detailed knowledge on the behavior of the energy functional on these orbits can be used to discuss positive energy theorems.Comment: 13 pages Latex file, agrees with published version, v2: additional paragraphs and references in the introduction and conclusion section

Notes on the BMS group in three dimensions: II. Coadjoint representation

The coadjoint representation of the BMS$_3$ group, which governs the covariant phase space of three-dimensional asymptotically flat gravity, is investigated. In particular, we classify coadjoint BMS$_3$ orbits and show that intrinsic angular momentum is free of supertranslation ambiguities. Finally, the link with induced representations upon geometric quantization is discussed.Comment: 22 pages, references added, accepted for publication in JHEP. v3: Minor typos corrected, matches published versio