Nonabelian gauge field dynamics on matrix D-branes

Abstract

We construct a calculational scheme for handling the matrix ordering problems connected with the appearance of D-brane positions taking values in the same Lie algebra as the nonabelian gauge field living on the D-brane. The formalism is based on the use of an one-dimensional auxiliary field living on the boundary of the string world sheet and taking care of the order of the matrix valued fields. The resulting system of equations of motion for both the gauge field and the D-brane position is derived in lowest order of the $\alpha'$ -expansion.