P-p′ strings in M(atrix) theory

We study the off-diagonal blocks in the M(atrix) model that are supposed to correspond to open strings stretched between a Dp-brane and a Dp′-brane. It is shown that the spectrum, including the quantum numbers, of the zero modes in the off-diagonal blocks can be determined from the index theorem and unbroken supersymmetry, and indeed reproduces string theory predictions for p-p′ strings. Previously the matrix description of a longitudinal fivebrane needed to introduce extra degrees of freedom corresponding to 0-4 strings by hand. We show that they are naturally associated with the off-diagonal zero modes, and the supersymmetry transformation laws and low energy effective action postulated for them are now derivable from the M(atrix) theory.