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

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