Potentials between D-branes in a supersymmetric model of space-time foam

We study a supersymmetric model of space-time foam with two stacks each of eight D8-branes with equal string tensions, separated by a single bulk dimension containing D0-brane particles that represent quantum fluctuations. The ground-state configuration with static D-branes has zero vacuum energy, but, when they move, the interactions among the D-branes and D-particles due to the exchanges of strings result in a nontrivial, positive vacuum energy. We calculate its explicit form in the limits of small velocities and large or small separations between the D-branes and/or the D-particles. This nontrivial vacuum energy appears as a central-charge deficit in the noncritical stringy sigma model describing perturbative string excitations on a moving D-brane. These calculations enable us to characterize the ground state of the D-brane/D-particle system, and provide a framework for discussing brany inflation and the possibility of residual dark energy in the present-day Universe.