On the quantization of folded strings in non-critical dimensions

TL;DR

This paper introduces a method to quantize folded strings in non-critical dimensions by placing massive particles at folding points, enabling calculation of quantum spectra and Regge intercepts independent of target space dimension.

Contribution

It proposes a novel regularization technique for quantizing folded strings using massive particles at folding points, allowing explicit spectrum and intercept calculations.

Findings

Intercepts are 1 for open and 2 for closed strings, independent of target space dimension.

The method successfully computes quantum fluctuation spectra around rotating strings.

Finite masses at folding points introduce calculable corrections to string properties.

Abstract

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are $a=1$ and $a=2$ for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.