We consider gauge/gravity correspondence between maximally supersymmetric Yang-Mills theories in (p+1) dimensions and superstring theories on the near-horizon limit of the Dp-brane solutions, with general p. Even though there is no conformal symmetry when p is not equal to 3, supergravity analysis suggests that at strong ‘t Hooft coupling, certain operators have power-law correlators, with powers different from the free-field values. On the other hand, it has not been understood how the free-field results can be obtained from the gravity side. In this work, we derive free-field correlators of gauge theories by considering superstrings on highly curved backgrounds. Our approach is based on the “string-bit” picture. We use the fact that the limit of weak ‘t Hooft coupling corresponds to the limit of weak string tension, in which the interaction between string bits can be ignored.