Two Virasoro symmetries in stringy warped AdS$_3$

TL;DR

The paper analyzes warped AdS$_3$ spacetimes arising from two 3D truncations of type IIB supergravity, proving that a non-dynamical subsector has the same covariant phase space as AdS$_3$ gravity and that this yields a Virasoro$\times$Virаsоро asymptotic symmetry (with Virasoro$\times$Kač–Moody as an alternative). It then extends the discussion to the full linearized phase space, showing that, provided bulk traveling waves are absent or controlled, the Virasoro symmetries extend to propagating modes, implying a semi-classical 2D CFT dual for warped AdS$_3$. The work relies on a precise mapping of symplectic structures via a boundary term $\boldsymbol{Y}$, enabling exact charge correspondences between warped and unwarped AdS$_3$ under standard boundary conditions. The results illuminate the holographic structure of warped AdS$_3$, clarify stability constraints, and raise important questions about positivity, non-linear extensions, and potential string-theoretic completions.

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 $\times$ Kač-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.