$0$, $1$, and $0$ respectively. This expression implies those operators are primary fields with the U(1) charge $0$ and the superconformal weight $h$. Especially the case $\Psi=T$ implies a vanishing of the total central charge for any $d$. Moreover the BRST supercurrent $j_B(Z)$ and the ghost number supercurrent $j_{\rm gh}(Z)$ in  are primary fields. In this sense, the supercurrents  in this effective theory are [*covariant*]{} in the quantum level and this desired feature suggests our construction in  is reliable.

For another relations between various operators, we have (also for any $d$), $$\eqalign{
 &G(Z_a)\overline G(Z_b)\sim
 {1\over{2Z_{ab}}}\left(\theta_{ab}^-D_b^+-\theta_{ab}^+D_b^-\right)
 J(Z_b)
 +{{\theta_{ab}^-\theta_{ab}^+}\over{Z_{ab}}}
 \,T(Z_b),
\cr
 &G(Z_a)G(Z_b)\sim0,
\cr
 &\overline G(Z_a)\overline G(Z_b)\sim0,
\cr
 &J(Z_a)J(Z_b)\sim0,
\cr
 &J(Z_a)G(Z_b)\sim
  {{\theta_{ab}^-\theta_{ab}^+}\over{Z_{ab}}}\,G(Z_b),
\cr
 &J(Z_a)\overline G(Z_b)\sim
  -{{\theta_{ab}^-\theta_{ab}^+}\over{Z_{ab}}}\,\overline G(Z_b).
\cr
}
\eqn\foureleven$$ Surprisingly, in the above operator algebra, no quantum anomalous term appears and it coincides with the classically expected form. In the case of $N=0$ and $N=1$ cases \[,\], on the other hand, the quantum anomalous terms vanish only at $d=-2$ and $d=\pm\infty$ respectively. The algebra in  and  form a kind of the topological conformal algebra or the twisted $N=4$ superconformal algebra \[,\]. Therefore, in the $N=2$ super-Liouville theory, the super-coordinate BRST supercurrent algebra gives a representation of a $N=2$ superfield extension of the 