Light-Cone Gauge String Field Theory in Noncritical Dimensions

We study light-cone gauge string field theory in noncritical space-time dimensions. Such a theory corresponds to a string theory in a Lorentz noninvariant background. We identify the worldsheet theory for the longitudinal coordinate variables $X^{\pm }$ and study its properties. It is a CFT with the right value of Virasoro central charge, using which we propose a BRST invariant formulation of the worldsheet theory.