Evidence for Gauge/Gravity Correspondence for D$p$-branes at Weak 't Hooft Coupling

We consider gauge/gravity correspondence for general Dp-branes with $0\le p\le 4$, namely, the duality between the (p+1)-dimensional maximally supersymmetric Yang-Mills theory and superstring theory on the near-horizon limit of the Dp-brane solution. It has been known that in the large N gauge theory at zero temperature and strong 't Hooft coupling, the two-point functions of operators corresponding to supergravity modes obey power-law, with a power different from the free-field value when $p\neq 3$. In this work, we show that the free-field result of gauge theory can be reproduced from the bulk string theory, for the two-point function of an operator Tr(Z^J), where Z is a complex combination of two scalar fields. We assume the spatial direction of worldsheet is discretized into J bits, and use the fact that these bits become independent particles when string tension is zero.