  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 SYM vertex operators and one Ramond-Ramond $C$-field vertex operator:
$<V_{C}V_{\phi} V_AV_A>$. 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
S-matrix elements of $<V_{C}V_{\phi} V_AV_A>$. We comment on close
intertwinedness of an open string and a closed string that must be behind the
matching.
