CASIMIR FORCES BETWEEN BEADS ON STRINGS AND MEMBRANES

We develop a general formalism to calculate the force between beads at tached to a flat d-dimensional membrane due to the quantum fluctuation s of the membrane. The interaction potential is derived as a function of d and the membrane energy density, tension, stiffness and temperatu re. We find that the induced interactions turn off when d exceeds a ce rtain critical dimension. The potential is attractive in all cases whe re it is non-zero and at finite temperature falls off exponentially fo r large distances.