forms a topological conformal algebra \[,\], which appears in two-dimensional topological (conformal) field theories \[,\]. This observation was reported in our previous communication \[\].

Firstly we change the normalization of the Liouville superfield as $$\Phi(Z)\longrightarrow{2\over\sqrt{d-1}}\Phi(Z).
\ee$$ Thus the correlation function in  changes to $$\VEV{\Phi\left(Z_a\right)\Phi\left(Z_b\right)}
  =\ln Z_{ab},
\ee$$ and the effective BRST supercurrent changes to $$\eqalign{
 j_B(Z)&=C(Z)\left(T^X+T^{\rm Liouville}+{1\over2}T^{\rm gh}\right)
\cr
 &\quad+{1\over4}D^-\left[C\left(D^+C\right)B\right]
       +{1\over4}D^+\left[C\left(D^-C\right)B\right].
\cr
}
\ee$$ In the above expression, we defined the Liouville energy-momentum tensor: $$T^{\rm Liouville}={1\over2}D^-\Phi D^+\Phi+\kappa\partial\Phi,
\ee$$ where $\kappa$ satisfies $$\kappa^2={{1-D}\over4}.
\ee$$

The BRST charge in the $N=2$ super-Liouville theory thus is given by $$Q_B=\int DZ\,C\left(T^X+T^{\rm Liouville}+{1\over2}T^{\rm gh}\right),
\ee$$ and, as we will see, it satisfies $Q_B^2=0$ for any $d$. Furthermore we will also see $$T(Z)=\left\{Q_B,B(Z)\right\},
\eqn\fourseven$$ where the total energy momentum tensor $T$ is defined by $$T=T^X+T^{\rm gh}+T^{\rm Liouville}.
\ee$$ At this point we examine the BRST supercurrent algebra in $N=2$ super-Liouville theory. We change the notation as $$\eqalign{
 &T(Z)\equiv T(Z),
\cr
 &G(Z)\equiv j_B(Z),
\cr
 &\overline G(Z)\equiv B(Z),
\cr
 &J(Z)\equiv j_{\rm ghost}(Z).
\cr
}
\eqn\fournine$$ For the superconformal properties, the relevant operator product expansion is (for any $d$), $$\eqalign{
 T(Z_a)\Psi(Z_b)&\sim
 h\,{{\theta_{ab}^-\theta_{ab}^+}\over{Z_{ab}^2}}\,\Psi(Z_b)
 +{1\over{2Z_{ab}}}\left(\theta_{ab}^-D_b^+-\theta_{ab}^+D_b^-\right)
 \Psi(Z_b)
\cr
 &\quad+{{\theta_{ab}^-\theta_{ab}^+}\over{Z_{ab}}}
 \,\partial_{z_b}\Psi(Z_b),
\cr
}
\eqn\fourten$$ where $\Psi=T$, $G$, $\overline G$, and $J$ with $h=1$, 