On the dynamics of BMN operators of finite size and the model of string bits

We consider the discretization effects of a string-bit model simulating the near-BMN operators in the super–Yang–Mills model. The fermionic sector of this model is altered by the so called species doubling. We analyze the possibilities to cure this disease and propose an alternative formulation of the fermionic sector free from the above drawbacks. Also we propose a formulation of string bits with exact supersymmetry, which produces however an even number of continuous strings in the limit $J\to \mathrm{\infty }$.