Covariant Currents in N=2 Super-Liouville Theory

TL;DR

This paper analyzes anomalies and covariant currents in N=2 super-Liouville theory, revealing a superfield extension of the topological conformal algebra that suggests a topological nature of the theory.

Contribution

It constructs covariant BRST and ghost number supercurrents and shows the supercurrent algebra forms a universal superfield extension of the topological conformal algebra.

Findings

Supercurrent algebra forms a superfield extension of the topological conformal algebra.

The algebra holds for arbitrary conformal matter and dimensions.

Indicates a topological nature of N=2 supergravity in two dimensions.

Abstract

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 {\it arbitrary\/} type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is very 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.