i) no appearance of a correction term due to the Liouville field in the ghost number supercurrent $j_{\rm gh}(Z)$ in  and, ii) no appearance of a divergence correction term in the expression of BRST supercurrent $j_B(Z)$ in . The origins of these facts are respectively, i) a vanishing of the ghost number anomaly in $N=2$ theory , ii) no appearance of the BRST anomaly which is not proportional to $d-2$ in . In fact, as is discussed in the following section, these two facts might be related each other.

We regard the whole set of the partition function  and , and the effective supercurrents in  as the effective theory of the two-dimensional $N=2$ supergravity, i.e., $N=2$ super-Liouville theory. The advantage of this effective theory is that we can use propagators in a flat space-time, like . Although the replacement $2-d\rightarrow1-d$ in the current operator construction in  is [*ad hoc*]{}, we will check the covariance of those supercurrents by using the operator product expansion (OPE) in the next section. This shift of the parameter, $2-d\rightarrow1-d$ also appeared as the ansatz in \[\].

BRST supercurrent algebra and the topological conformal algebra
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In this section, we show that our effective supercurrents in  