We construct the world-sheet interface which preserves space-time
supersymmetry in type II superstring theories in the Green-Schwarz formalism.
This is an analog of the conformal interface in two-dimensional conformal field
theory. We show that a class of the supersymmetric interfaces generates
T-dualities of type II theories, and that these interfaces have a geometrical
interpretation in the doubled target space. We compute the partition function
with a pair of the supersymmetric interfaces inserted, from which we read off
the spectrum of the modes coupled to the interfaces and the Casimir energy
between them. We also derive the transformation rules under which a set of
D-branes is transformed to another by the interface.Comment: 1+23 pages, 1 figure; (v2) added comments, made changes in
presentatio