Superfluid films in porous media

The superfluid transition of /sup 4/He films adsorbed in porous media is analyzed with use of a generalization of the Kosterlitz-Thouless theory appropriate to connected surfaces. Topological excitations with quanta of circulation around loops which enclose the pore space are identified. On large length scales these excitations are described by a Villain model with coupling constant determined by the geometry of the pore space and the effect of vortex excitations. For a range of geometries the onset of the 3D critical region is determined by the Kosterlitz-Nelson universal jump line.