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

TL;DR

The paper addresses whether Polchinski-Strominger–type (PS) effective string theories acquire spectral corrections at all orders in the $R^{-1}$ expansion. It builds an exactly conformal Polyakov-Liouville-type action $S_{(2)}$ that extends PS theory to all orders, derives the EOM, $T_{--}$, and Virasoro generators, and shows that the spectrum remains identical to the free bosonic string in all dimensions. It first confirms the absence of $R^{-3}$ corrections and, using a covariant all-order framework, demonstrates that the ground state and excited-state energies reproduce the free-string results to all orders considered; with Drummond’s results ruling out $R^{-4}$ and $R^{-5}$ corrections, the universality extends through these orders. The work thus provides a covariant, all-order justification for the spectral universality of conformal PS-type effective strings and offers a framework to compare with Lüscher-Weisz analyses and numerical simulations.

Abstract

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 all orders 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 spectrum of 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 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 \emph{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.