Light-cone gauge superstring field theory in linear dilaton background

The Feynman amplitudes of light-cone gauge superstring field theory suffer from various divergences. In order to regularize them, we study the theory in linear dilaton background $\Phi =-iQX^1$ with the number of spacetime dimensions fixed. We show that the theory with the Feynman $i\varepsilon\,(\varepsilon>0)$ and $Q^{2}>10$ yields finite results.