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    Paper   IPM / P / 14181
       School of Physics
      Title: Symplectic and Killing Symmetries of AdS3 Gravity: Holographic vs Boundary Gravitons
      Author(s):
    1 . G. Compère
    2 . P. Mao
    3 . A. Seraj
    4 . M.M. Sheikh-Jabbari
      Status: Published
      Journal: JHEP
      Vol.: 1601
      Year: 2016
      Pages: 080
      Supported by: IPM
      Abstract:
    The set of solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions is known to be a family of metrics labeled by two arbitrary periodic functions, respectively left and right-moving. It turns out that there exists an appropriate presymplectic form which vanishes on-shell. This promotes this set of metrics to a phase space in which the Brown-Henneaux 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 right-moving function to zero and restricting the choice of orbits, one can take a near-horizon 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 near-horizon geometry can be obtained as a limit of the bulk symplectic symmetries.

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