The classical and the quantum massive string model based on a modified BDHP action is analyzed in the range of dimensions 1 < d < 25. The discussion concerning classical theory includes a formulation of the geometrical variational principle, a phase-space description of the two-dimensional dynamics, and a detailed analysis of the target space geometry of classical solutions. The model is quantized using "old" covariant method. In particular an appropriate construction of DDF operators is given and the no-ghost theorem is proved. For a critical value of one of free parameters of the model the quantum theory acquires an extra symmetry not present on the classical level. In this case the quantum model is equivalent to the noncritical Polyakov string and to the old Fairlie-Chodos-Thorn massive string.
The classical and quantum model of high spin particles is analyzed within the manifestly covariant framework. The model is obtained by supplementing the standard Lagrange function for relativistic point particle by additional terms governing the dynamics of internal degrees of freedom. They are described by C(3, 1) Clifford algebra (Majorana) spinors. The covariant quantization leads to the spectrum of the particles with the masses depending on their spins. The particles (and anti-particles) appear to be orphaned as their potential anti-particle partners are of different mass.
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.
It is shown that superconformal Lie superalgebras contain a Clifford algebra structure. This is used to present a classification of these algebras under the following assumptions: only fields with (half-)integer conformal dimension between 2 and 1/2 , and a nonzero central element. It turns out that the number of supersymmetry generators must be less than or equal to 4. More generally, the so(N) series, as well as some nonassociative algebras connected to S7, also have a natural place in this Clifford algebra framework.
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