the sense that the (super-)coordinate BRST current algebra gives a realization of an $N=2$ superfield extension of the topological conformal algebra \[,\] for arbitrary type of conformal matter.

In this paper we want to analyze in detail the appearance of this topological conformal algebra in the case of $N=2$ super-Liouville theory by constructing an effective theory based on anomalous identities associated with the BRST and ghost number symmetries. The finite renormalization of the coupling constant will be interpreted as a one-loop order effect of the BRST invariant measure. The relation with the critical string will be also commented.

The organization of the paper is as follows. In Section 2, we compute the BRST and ghost number anomalies in the $N=2$ supergravity in the superconformal gauge, by using the path integral representation \[\]. The $N=2$ super-Liouville theory is constructed in Section 3 with a consideration on the covariant BRST and ghost number supercurrents. In Section 4 we derive the topological conformal algebra. In section 5 there are some conclusions and there is an Appendix about some basic facts of the $N=2$ superfield formalism.

BRST and ghost number anomalies in $N=2$ supergravity
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In this section, we compute anomalies associated with the 