Abstract
In this paper we discuss D-branes in the Melvin background and its supersymmetric generalizations. In particular we determine the D-brane spectra in these backgrounds by constructing their boundary states explicitly, where some of the D-branes are supersymmetric. The results sensitively depend on whether the value of magnetic flux in the Melvin background is rational or irrational. For the rational case the D-branes are regarded as the generalizations of fractional D-branes in abelian orbifolds n/N of type-II or type-0 string theory. For the irrational case we found a very limited spectrum. Since the background includes the non-trivial H-flux, the D-branes will provide interesting examples from the viewpoint of the non-commutative geometry.
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