Non-Critical Light-Cone String

TL;DR

This paper constructs a non-critical light-cone string model in dimensions 1 to 25, analyzing its algebraic structure, spin content, and showing its equivalence to critical string models within this range.

Contribution

It introduces a direct light-cone quantization approach for non-critical strings and provides explicit formulas for spin spectra, expanding understanding of string models outside critical dimensions.

Findings

Model constructed in dimensions 1<D<25

Explicit character formulas for D=4 strings

Equivalence to critical and Nambu-Goto strings in this range

Abstract

The free non-critical string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<D<25$. The longitudinal degrees of freedom are described by an abstract Verma module. The central charge of this module is restricted by the requirement of the closure of the nonlinear realization of the Poincare algebra. The spin content of the model is analysed. In particular for D=4 the explicit formulae for the character generating functions of the open and closed massive strings are given and the spin spectrum of first 12 excited levels is calculated. It is shown that for the space-time dimension in the range $1<D<25$ the non-critical light-cone string is equivalent to the critical massive string and to the non-critical Nambu-Goto string.