Super Liouville Theory with Boundary
  We study N=1 super Liouville theory on worldsheets with and without boundary. Some basic correlation functions on a sphere or a disc are obtained using the properties of degenerate representations of superconformal algebra. Boundary states are classified by using the modular transformation property of annulus partition functions, but there are some of those whose wave functions cannot be obtained from the analysis of modular property. There are two ways of putting boundary condition on supercurrent, and it turns out that the two choices lead to different boundary states in quality. Some properties of boundary vertex operators are also presented. The boundary degenerate operators are shown to connect two boundary states in a way slightly complicated than the bosonic case. 
Takeshi Fukuda and Kazuo Hosomichi