Spectrum to all orders of Polchinski-Strominger Effective String Theories of the Drummond Type

Drummond had proposed four actions for Polchinski-Strominger effective string theories at order $R^{-6}$, where $2\pi R$ is the length of the (closed) string

. In \cite{covariant} it had been shown, based on covariance arguments, that only two of them are independent. We analyse the spectral content of effective string theories with these two actions. We show that the inclusion of these actions does not yield corrections to the spectrum of Nambu-Goto theory \cite{Arv}.