Two Virasoro symmetries in stringy warped AdS3

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS(3) solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS(3). Consequently, for each consistent choice of boundary conditions in AdS(3), we can define a consistent phase space in warped AdS(3) with identical conserved charges. This way, we easily obtain a Virasoro x Virasoro asymptotic symmetry algebra in warped AdS(3); two different types of Virasoro x Kac-Moody symmetries are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro x Virasoro asymptotic symmetries can be extended to the entire (linearised) phase space. This implies that, at least at semi-classical level, consistent theories of gravity in warped AdS3 are described by a two-dimensional conformal field theory, as long as stability is not an issue.