On string momentum in effective string theories

Understand

Centre of mass momentum for strings is an important ingredient in the calculation of the spectrum of string theories.

• It is calculated by the N\"other prescription for two types of conformally invariant effective string theories of the Polchinski-Strominger type.
• One is the so called Polyakov-Liouville theory \cite{liouville} and the other an extension of the original Polchinski-Strominger action analysed upto order $R^{-3}$ where $2\pi R$ is the length of the string.
• In the first case analysis is carried out to order $R^{-2}$ and in the second case to order $R^{-3}$.