  We propose a theory of the spin dynamics of frustrated quantum
antiferromagnets, which is based on an effective action for a plaquette
embedded in a self-consistent bath. This approach, supplemented by a low-energy
projection, is applied to the kagome antiferromagnet. We find that a
spin-liquid regime extends to very low energy, in which local correlation
functions have a slow decay in time, well described by a power law behaviour
and $\omega/T$ scaling of the response function: $\chi''(\omega)\propto
\omega^{-\alpha}F(\omega/T)$.
