We propose a dimensional regularization scheme to deal with the divergences caused by colliding supercurrents inserted at the interaction points, in the light-cone gauge NSR superstring field theory. We formulate the theory in $d$ dimensions and defi
ne the amplitudes as analytic functions of $d$. With an appropriately chosen three-string interaction term and large negative $d$, the tree level amplitudes for the (NS,NS) closed strings can be recast into a BRST invariant form, using the superconformal field theory proposed in Ref.[arXiv:0911.3704]. We show that in the limit $d to 10$ they coincide with the results of the first quantized theory. Therefore we obtain the desired results without adding any contact interaction terms to the action.
Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory for the long
itudinal variables X^{pm}, psi^{pm}. We show that with the transverse variables and the ghosts combined, it is possible to construct a nilpotent BRST charge.
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.
