Constraints on effective Lagrangian of D-branes from non-commutative gauge theory

We consider the constraints on the effective Lagrangian of gauge fields on D-branes imposed by the compatibility of the description by non-commutative gauge theory with that by ordinary gauge theory in the presence of a constant B field background. It is argued that the constraints are in general derived without assuming the form of the field redefinition which relates the non-commutative gauge field to the ordinary one and their relation is rather regarded as a consequence of the compatibility. We then apply our argument to the two-derivative terms in bosonic string theory, and the consistency between the two descriptions is established by observing the necessity of gauge-invariant but B-dependent correction terms in the field redefinition which have not been considered previously. ∗ E-mail: [email protected] † E-mail: [email protected]