Title: Covariant Currents in N=2 Super-Liouville Theory Show Chinese title

Title: N=2超Liouville理论中的协变流urrent

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. Show Chinese abstract

Abstract: 基于异常计算的路径积分公式，我们分析了二维$N=2$超引力的有效理论，即$N=2$超Liouville理论。 我们计算了与BRST超电流和鬼数超电流相关的异常。 从这些异常表达式中，我们在有效理论中构造了协变的BRST和鬼数超电流。 然后我们证明了（超）坐标BRST电流代数形成了一个超场扩展的拓扑共形代数，适用于{\it 任意的/}类型的共形物质，或者用弦理论的语言来说，适用于任意时空维度。 这一事实与$N=0$和$N=1$（超）Liouville理论形成鲜明对比，在这些理论中，拓扑代数选出特定的维度值。 我们的观察表明二维$N=2$超引力作为量子理论具有拓扑性质。