A Fefferman-Graham-like expansion for null warped AdS(3)

TL;DR

This work develops a Fefferman–Graham–like expansion for metric modes in null warped AdS$_3$ by mapping them to AdS$_3$ solutions within a three-dimensional Einstein–Proca theory. The authors isolate the stress-tensor–relevant T-modes, derive their linear and nonlinear asymptotics, and show the renormalized on-shell action reduces to the AdS$_3$ result expressed via an auxiliary metric $ ilde{g}$. The holographic stress tensor couples to the boundary metric of this auxiliary AdS$_3$ and exhibits a conserved, symmetric form with the same conformal anomaly as AdS$_3$, hinting at two Virasoro-like asymptotic symmetries. The work also discusses extensions to non-linear effects, X-modes, and higher-dimensional generalizations as future directions. Overall, it clarifies the holographic dictionary for null warped AdS$_3$ and sets the stage for understanding warped AdS$_3$ black holes and Kerr/CFT connections.

Abstract

We consider null warped AdS(3) solutions of three-dimensional gravity coupled to a massive vector field. We isolate a certain set of non-propagating solutions to the equations of motion, which we argue are the ones relevant for understanding the stress tensor sector of the dual field theory. We construct a map from these modes to solutions of three-dimensional Einstein gravity with a negative cosmological constant, and thus show that they admit a Fefferman-Graham-like asymptotic expansion. We also compute the renormalized on-shell action for these modes at full non-linear level and propose that the dual stress-energy tensor couples to the boundary metric of the auxiliary AdS(3) spacetime. The holographic stress tensor we obtain is symmetric, conserved and its trace yields the same conformal anomaly as in AdS(3).