Abstract
A survey is given of the formulation of a σ-model describing an open string moving in general target space background fields and coupling to both a matrix-valued D-brane position and a matrix-valued gauge field on the D-brane. The equations of motion for the D-brane and the gauge field are derived from the conformal invariance condition on the string world sheet in lowest order of α′. The ordering problem of the involved matrices is solved. In addition to our previous work we discuss a con ict between the classical T-duality rules and renormalization. The calculation of the RG β-functions does not yield the mass term obtained by formal application of these rules in the case of target space separated D-brane copies.
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