A two-loop test of M(atrix) theory

We consider the scattering of two Dirichlet zero-branes in M(atrix) theory, Using the formulation of M(atrix) theory in terms of ten-dimensional super Yang-Mills theory dimensionally reduced to (0 + 1) dimensions, we obtain the effective (velocity-dependent) potential describing these particles. At one loop we obtain the well-known result for the leading order of the effective potential V-eff similar to v(4)/r(7), where v and r are the relative velocity and distance between the two zero-branes, respectively. A calculation of the effective potential at two loops shows that no renormalizations of the v(4) term of the effective potential occur at this order. (C) 1997 Elsevier Science B.V.