Spinning strings of the Neveu-Schwarz-Ramond type in 3, 4, 6, and 10 space-time dimensions

A model of a spinning string with an internal coordinate index is proposed and studied. When the action for this model is taken to be diagonal in this internal coordinate space and quantized in the light-cone gauge it is found to be Lorentz covariant in four-dimensional space-time provided that the internal coordinate space is four dimensional. This combination of space-time dimension, D, and internal coordinate space dimension, N, is just one of four possible sets, the other three corresponding to D = 3,6, and 10, precisely the same values for which it is possible to formulate Yang-Mills theories with simple supersymmetry. By comparing the number of propagating degrees of freedom at the zero-mass level in the open string bosonic and fermionic sectors it is found that a supersymmetric interpretation of this model is possible provided that all physical states in the bosonic sector have even G-parity and the ground-state spinor in the fermionic sector have positive chirality. A possible interpretation of the connection between the N components of each of the D space-time coordinates is presented on the basis that the space-time coordinates are scalars in the internal coordinate space. This interpretation would appear to be reasonable given the fact that the field variables in the Lagrangian density do not necessarily have to represent physically measurable quantities but can, instead, only represent physically measurable quantities when combined in some manner, the simplest of which being a linear combination. The Lagrangian density simply produces the equations of motion and the constraint equations for the independent variables, only linear combinations of which represent the four dimensions of physical space-time.