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The spectrum of a Polchinski-Strominger type effective string theory,extended to all orders, herein called an effective string theory of the\emph{Polyakov-Liouville Type} (for obvious reasons) is investigated to allorders in the small parameter $R^{-1}$. Here $R$ is the length of the\emph{closed} string. It is established that to \emph{all orders} the spectrumof this theory is \emph{identical} to that of the free bosonic string theory.While the latter is consistent only in the critical dimension $D_c=26$, the PS-type effective string theories are by construction consistent in \emph{all}dimensions. This work extends earlier results by Drummond, and, by Hari Dassand Matlock to order $R^{-3}$. When combined with Drummond's results aboutabsence of candidate actions at orders $R^{-4},R^{-5}$, our results imply thatthe spectrum of \emph{all} effective string theories coincides with that offree bosonic string theories to order $R^{-5}$. This agrees with the recentresults by Aharony and Karzbrun. Our work is the first all order analysis ofany effective string theory.

Spectrum to all orders of Polchinski-Strominger {Effective} String Theory of Polyakov-Liouville Type