Free energies and probe actions for near-horizon D-branes and D1+D5 system

By working with the free energy for the type II supergravity near-horizon solution of N coincident non-extremal Dp-branes, we study the transitions among the non-conformal Dp-brane system, the perturbative super-Yang-Mills theory and a certain system associated with M theory. We derive a relation between this free energy and the action of a Dp-brane probe in the N Dp-brane background. Constructing the free energy for the five-dimensional black hole labeled by the D1-brane and D5-brane charges, we find the similar relation between it and the action of a D1 or D5 brane probe in the D1 + D5 brane background. These relations are explained by the massive open strings stretched between the relevant D-branes.