# Two Virasoro symmetries in stringy warped AdS$_3$

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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 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 (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.
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https://hal-cea.archives-ouvertes.fr/cea-01541491
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### Citation

Geoffrey Compère, Monica Guica, Maria J. Rodriguez. Two Virasoro symmetries in stringy warped AdS$_3$. Journal of High Energy Physics, Springer, 2014, pp.012. ⟨10.1007/JHEP12(2014)012⟩. ⟨cea-01541491⟩

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