Conformal symmetry and central charges in 4 dimensions (original) (raw)

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.