of the action of $\widetilde X^\mu(z)$ with replacement $\sigma\rightarrow\sigma_0$. Thus, up to the one-loop order, we have additional contribution from the Liouville part itself, $${1\over16\pi}\int d^2x
   \partial\sigma_0\partialbar\sigma_0
  .
\ee$$ We regard this factor as the one-loop finite renormalization effect. Adding this effect to the original contribution from , and after a covariantization, we finally have $$\eqalign{
  &\int\Di\sigma
      \Di\phi^+\Di\overline\phi^+\Di\phi^-\Di\overline\phi^-\Di\phi
\cr
  &\times\exp\left\{
   -{1-d\over16\pi}\int d^2x\left[\partial\sigma\partialbar\sigma
                           +\partial\phi\partialbar\phi
                           -\phi^+\partialbar\phi^-
                           -\phi^-\partialbar\phi^+
                           +({\rm c.\ c.})\right]
   \right\},
\cr
}
\eqn\threeforteen$$ where we have rewritten $\sigma_0$ as $\sigma$ and taken a naive integration measure $\sigma$ for the Liouville field, since we already include the (one-loop) quantum effect of $e^{\sigma/2}$. We should note here the coefficient in , $2-d$, changes to $1-d$ in . Since the action in  has the same form as the matter supermultiplet $X^\mu(Z)$, the correlation function of the Liouville superfield $\Phi$ is given by $$\VEV{\Phi\left(Z_a\right)\Phi\left(Z_b\right)}
  ={4\over d-1}\ln Z_{ab}.
\eqn\threefifteen$$ As the effective covariant supercurrents in the partition function , we may take  with a replacement $2-d\rightarrow 1-d$, i.e., $$\eqalign{
  &j_B(Z)\equiv C\left(T^X+{1\over2}T^{\rm gh}\right)
   +{d-1\over4}C
    \left({1\over2}\Diminus\Phi\Diplus\Phi+i\partial\Phi\right)
\cr
  &\qquad\qquad
  +{1\over4}\Diminus\left[C\left(\Diplus C\right)B\right]
  +{1\over4}\Diplus\left[C\left(\Diminus C\right)B\right],
\cr
  &j_{\rm gh}(Z)\equiv-BC.
}
\eqn\threesixteen$$ We comment on the differences of  from the analogous construction for the $N=0$ and $N=1$ (super-)Liouville cases \[,\]. The differences are 