ON NON-ABELIAN GENERALIZATION OF THE BORN-INFELD ACTION IN STRING THEORY

We point out that the part of the tree-level open string effective act ion for the non-abelian vector field which depends on the field streng th but not on its covariant derivatives is not defined unambiguously. We show that if one adopts the definition under which one drops all te rms depending on all possible products (symmetrised or antisymmetrised ) of covariant derivatives then this part of the action is given by th e symmetrised trace of the direct non-abelian generalisation of the Bo rn-Infeld action, We discuss some possible applications to D-brane dyn amics. (C) 1997 Elsevier Science B.V.