Abstract
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 $\times$ Virasoro asymptotic symmetry algebra in warped AdS$_3$; two different types of Virasoro $\times$ Ka\v{c}-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 $\times$ Virasoro asymptotic symmetries can be extended to the entire (linearized) phase space. This implies that, at least at semi-classical level, consistent theories of gravity in warped AdS$_3$ are described by a two-dimensional conformal field theory, as long as stability is not an issue.
Highlights
We study the phase space of these theories when propagating modes are included
The part of the geometry that appears to play the key role in the duality is a warped AdS3 factor — whose structure is that of a U(1) fibre over AdS2 — which is universally present in the near-horizon region of extremal black holes [16]
Our first result is that the symplectic form of certain theories admitting warped AdS3 solutions, when restricted to a non-dynamical subsector, is exactly equal to the symplectic form of pure Einstein gravity in three dimensions
Summary
We begin this section by reviewing two consistent truncations of type IIB supergravity theory to three dimensions that were worked out in [39] and that will be the main examples we use in this article. These truncations are interesting because they contain a rich spectrum of warped analogues of the BTZ black string as solutions, i.e. solutions characterized by two independent conserved charges that can be interpreted as excited states above the warped AdS3 vacuum.. In the last two subsections, we review the covariant phase space formalism [51, 52] for the construction of the symplectic form and conserved charges in diffeomorphisminvariant theories
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