mode and, $\phi^\pm$ and $\phi$ are their $N=2$ superpartners.

The BRST supercurrent and ghost number supercurrent anomalies will depend on the Liouville mode $\sigma$ and their $N=2$ superpartners. As we are working in a path integral in the components, we should construct the integration variables depending on $\sigma$, $\phi^\pm$, and $\phi$ such that the integration measure is invariant under the supercoordinate transformations. This program have some difficulties, for $N=1$, see for example \[\]. Here instead we are going to use the following strategy. Let us forget about the anomalous character of the super-Weyl and the chiral transformations. By using these symmetries, we can fix the gauge $$\eqalign{
  &e_\mu^a=e^{\sigma/2}\delta^a_\mu,
\cr
  &\chi^\pm_\mu=0,
\cr
  &A_\mu=0.
\cr
}
\ee$$ In this way, the BRST supercurrent and ghost number supercurrent anomalies will depend only on the Liouville mode. When we consider the effect of the super-Weyl and the chiral anomalies, the remaining components of the gravitino and the U(1) gauge field should appear in various anomalies. Here we [*assume*]{} that we are actually using a regularization that is invariant under the super-coordinate and the gauge transformations. Especially, we assume the invariance under the [*global*]{} super transformation: $$\eqalign{
  &\delta\sigma=i\left(\alpha^+\phi^--\alpha^-\phi^+\right),
\cr
  &\delta\phi=\alpha^-\phi^++\alpha^+\phi^-,
\cr
  &\delta\phi^\pm
  =\alpha^\pm\left(\partial\phi\pm i\partial\sigma\right).
\cr
