Covariant currents in N = 2 super-Liouville theory

Based on a path-integral prescription for anomaly calculation, we analyze an effective theory of the two-dimensional N = 2 supergravity, i.e. N = 2 super-Liouville theory. We calculate the anomalies associated with the BRST supercurrent and the ghost-number supercurrent. From those expressions of anomalies, we construct covariant BRST and ghost-number supercurrents in the effective theory. We then show that the (super-)coordinate BRST current algebra forms a superfield extension of the topological conformal algebra for an arbitrary type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is in great contrast with N = 0 and N = 1 (super-)Liouville theory, where the topological algebra singles out a particular value of dimensions. Our observation suggests a topological nature of the two-dimensional N = 2 supergravity as a quantum theory.