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Paper IPM / Physic / 14181  


Abstract:  
The set of solutions to the AdS3 Einstein gravity with BrownHenneaux boundary conditions is known to be a family of metrics labeled by two arbitrary periodic functions, respectively left and rightmoving. It turns out that there exists an appropriate presymplectic form which vanishes onshell. This promotes this set of metrics to a phase space in which the BrownHenneaux asymptotic symmetries become symplectic symmetries in the bulk of spacetime. Moreover, any element in the phase space admits two global Killing vectors. We show that the conserved charges associated with these Killing vectors commute with the Virasoro symplectic symmetry algebra, extending the Virasoro symmetry algebra with two U(1) generators. We discuss that any element in the phase space falls into the coadjoint orbits of the Virasoro algebras and that each orbit is labeled by the U(1) Killing charges. Upon setting the rightmoving function to zero and restricting the choice of orbits, one can take a nearhorizon decoupling limit which preserves a chiral half of the symplectic symmetries. Here we show two distinct but equivalent ways in which the chiral Virasoro symplectic symmetries in the nearhorizon geometry can be obtained as a limit of the bulk symplectic symmetries.
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