this sense, the absence of a total divergent anomaly in  is an intrinsic feature of the $N=2$ theory and suggests the topological nature of $N=2$ theory as a quantum theory.

We can also summarize the ghost number anomaly in terms of the supercurrent: $$\partialbar\VEV{j_{\rm gh}(Z)}=0.
\eqn\twofortynine$$ The anomalous identities,  and  will play an important role when we construct the effective covariant supercurrents in $N=2$ super-Liouville theory.

$N=2$ super-Liouville theory and the covariant supercurrents
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In the previous section, we saw that the various anomalies appear through the $\sigma$-dependences in the integration measure . Here we try to construct an effective theory which is supposedly equivalent with the original $N=2$ supergravity , by incorporating the effect of anomalies. Firstly, following a standard procedure to produce the Wess–Zumino term in the string theory \[\], we repeat an infinitesimal transformation of the integration variables. For example, we change $\widetilde X^\mu$ as $$\widetilde X^\mu\longrightarrow
  \left(1+{\sigma\over2}dt\right)\widetilde X^\mu.
\eqn\threeone$$ By repeating this infinitesimal transformation up to a finite $t$, the kinetic operator of $\widetilde X^\mu$ changes to $$e^{-\sigma(1-t)/2}\partial\partialbar e^{-\sigma(1-t)/2},
\ee$$ thus all the $\sigma$ dependences in  and  disappear at $t=1$.

On the other hand, from the master formula , the change of variable in  generates the 