More on closed string induced higher derivative interactions on D-branes

In our continued efforts of matching full string computations with the corresponding effective field theory computations, we evaluate string theory correlators in closed forms. In particular, we consider a correlator between three super Yang-Mills vertex operators and one Ramond-Ramond C-field vertex operator: < VCV phi VAVA >. We show that the infinite number of massless poles of this amplitude can be reproduced by the Born-Infeld action, the Wess-Zumino terms, and their higher derivative corrections. More specifically, we find, up to an on-shell ambiguity, two scalar field and two gauge field couplings to all orders in alpha' such that the infinite number of massless poles of the field theory amplitude exactly match the infinite number of massless poles of the S-matrix elements of < VCV phi VAVA >. We comment on the close intertwinedness of an open string and a closed string that must be behind the matching.