New Spinor Field Realizations of the Non-Critical $W_3$ String

We investigate the new spinor field realizations of the $W_3$ algebra, making use of the fact that the $W_3$ algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora–Tyutin (BRST) charges of the spinor non-critical $W_3$ string.