Gauge Independent Trace Anomaly for Gravitons

TL;DR

This paper demonstrates that the trace anomaly for gravitons depends on gauge choice off-shell and introduces a gauge-independent method using Vilkovisky-DeWitt effective action, with explicit calculations on N-sphere backgrounds.

Contribution

It introduces a gauge-independent approach to compute the trace anomaly for gravitons off-shell, resolving gauge dependence issues present in traditional methods.

Findings

Trace anomaly depends on gauge when off-shell.

Vilkovisky-DeWitt effective action restores gauge independence.

Explicit calculations of trace anomalies on N-sphere backgrounds.

Abstract

We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off-shell. We then use the gauge independent Vilkovisky-DeWitt effective action to restore gauge independence to the off-shell case. Additionally we explicitly evaluate trace anomalies for some N-sphere background spacetimes.