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A two-loop test of M(atrix) theory. (English) Zbl 0925.81264

Summary: 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 \(V_{eff}\sim v^4/r^7\), 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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