Conformal Symmetry and Central Charges in 4 Dimensions

TL;DR

This paper investigates the trace anomaly in four-dimensional curved space, calculating contributions to central charges from ghosts and conformal factors, enhancing understanding of conformal symmetry and anomalies in 4D quantum field theories.

Contribution

It provides the first detailed computation of ghost contributions to central charges in 4D and explores their consistency with spin-2 mode contributions.

Findings

Ghost contributions satisfy Wess-Zumino consistency with spin-2 modes

Quantum conformal factor contributions to trace anomaly calculated

Enhanced understanding of conformal symmetry in 4D space

Abstract

The trace anomaly of matter in curved space generates an effective action for the conformal factor of the metric tensor in $D=4$ dimensions, analogous to the Polyakov action for $D=2$. We compute the contributions of the reparameterization ghosts to the central charges for $D=4$, as well as the quantum contribution of the conformal factor itself. The ghost contribution satisfies the necessary Wess-Zumino consistency condition only if combined with the spin-2 modes, whose contributions to the trace anomaly we also discuss.