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

TL;DR

This paper develops a Fefferman-Graham-like expansion for null warped AdS(3) solutions, linking them to standard AdS(3) gravity and analyzing the dual stress tensor in the holographic framework.

Contribution

It introduces a novel asymptotic expansion for null warped AdS(3) solutions and maps these to Einstein gravity solutions, advancing holographic stress tensor analysis.

Findings

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

Mapped non-propagating modes to Einstein gravity solutions

Derived a holographic stress tensor with AdS(3) conformal anomaly

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).