Holographic trace anomaly at finite temperature

TL;DR

This paper derives a coordinate transformation for AdS black holes, enabling the calculation of holographic stress tensors and trace anomalies, and interprets their radial dependence as RG flow in the boundary theory.

Contribution

It provides an exact transformation rule for AdS black holes to Fefferman-Graham coordinates, facilitating holographic stress tensor and trace anomaly calculations as functions of the radial coordinate.

Findings

Derived exact coordinate transformation rules.

Computed holographic stress tensor and trace anomaly.

Interpreted radial dependence as Wilsonian RG flow.

Abstract

We find an exact coordinate transformation rule from the $AdS_5$ Schwarzschild black hole in the Poincare and the global patch to the Fefferman-Graham coordinate system. Using these results, we evaluate the corresponding holographic stress tensor and trace anomaly of the boundary theory as a function of the radial coordinate. Following the AdS/CFT correspondence, we reinterpret the radial coordinate dependence of the trace anomaly as the Wilsonian renormalization group(RG) flow of the boundary theory.