Non-critical light-cone string

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.

High Spin Particles with Spin-Mass Coupling

“…According to (6) the Poisson brackets of the canonical Weyl variables are given as follows: The second class constraints of (7) relate the Weyl coordinates: G A = z A + z A = 0 and GĀ = zĀ + zĀ = 0. Their polarized counterparts (10) can be reexpressed in the following way:…”

Light-cone formulation and spin spectrum of non-critical fermionic string

“…We shall use the method developed in the case of the bosonic light-cone string [5]. It relies on the observation that, as far as the character generating function is concerned, the vector representation of Spin(d − 2) formed by the transverse excitation can be extended to a vector representation of Spin(d−1) by means of the Liouville excitations.…”

Free Strings in Non-Critical Dimensions

“…The proof of this fact based on the DDF operators technique was recently given in Ref. [4]. It should be also stressed that there exists yet another way of constructing this model.…”

“…The non-critical light-cone string briefly presented below was recently constructed in Ref. [4]. A similar construction motivated by the Liouville theory was also analysed by Marnelius in the context of non-critical Polyakov string [14].…”

“…Such construction was recently proposed in Ref. [4] and is briefly described in Section 4. In Section 5 some conclusions are presented.…”