3-dimensional holographic trace anomaly from AdS/CFT correspondence

TL;DR

This paper derives the energy-momentum tensor at the boundary of certain 4-dimensional AdS spacetimes, revealing how the 3D trace anomaly relates to volume and Ricci scalar within the AdS/CFT framework.

Contribution

It provides explicit formulas for the boundary energy-momentum tensor in Schwarzschild AdS4 and Taub-NUT-(A)dS4, linking 3D trace anomaly to geometric quantities.

Findings

Explicit energy-momentum tensor expressions for AdS4 and Taub-NUT-dS.

Trace anomaly expressed in terms of 3D volume and Ricci scalar.

Asymptotic series for general cases.

Abstract

We explicitly obtain energy-momentum tensor at the asymptotic 3-dimensional region of Schwarzschild AdS$_4$ and Taub-NUT-(A)dS$_4$ using the so-called `counter-term subtraction method' in Fefferman-Graham coordinate. The energy momentum tensor is presented in a closed form for the AdS$_4$ and for the special case of Taub-NUT-dS and in an asymptotic series for other cases. The result suggests that in light of AdS/CFT correspondence, the 3-dimensional trace anomaly can be expressed in terms of the 3-dimensional volume and Ricci scalar.