Constraints on effective Lagrangian of D-branes from non-commutative gaugetheory

It was argued that there are two different descriptions of the effective La grangian of gauge fields on D-branes by non-commutative gauge theory and by ordinary gauge theory in the presence of a constant B field background. In the case of bosonic string theory, however, it was found in;the previous w orks that the two descriptions are incompatible under the field redefinitio n which relates the non-commutative gauge field to the ordinary one found b y Seiberg and Witten. In this paper we resolve this puzzle to observe the n ecessity of gauge-invariant but B-dependent correction terms involving metr ic in the field redefinition which have not been considered before. With th e problem resolved, we establish a systematic method under the alpha' expan sion to derive the constraints on the effective Lagrangian imposed by the c ompatibility of the two descriptions where the form of the field redefiniti on is not assumed. (C) 2000 Elsevier Science B.V. All rights reserved.