The semi-classical energy of closed Nambu-Goto strings

TL;DR

This paper calculates semi-classical energy corrections for rotating closed Nambu-Goto strings, confirming previous results and revealing unphysical modes in the spectrum that lack physical excitations.

Contribution

It provides a semi-classical analysis of string energies, validating earlier findings and identifying unphysical modes in the spectrum of excitations.

Findings

Semi-classical corrections match Polchinski-Strominger results.

Unphysical modes are present in the spectrum.

Spectrum contains modes with no physical excitations.

Abstract

We compute semi-classical corrections to the energy of rotating closed Nambu-Goto strings. We confirm the results obtained by means of the Polchinski-Strominger action. We also show that in this semi-classical approximation, the spectrum of physical excitations contains modes that are unphysical non-perturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond.