A theorem on the power of supersymmetry in Matrix theory

For the so-called source-probe configuration in Matrix theory, we prove the following theorem concerning the power of supersymmetry (SUSY): let delta be a quantum-corrected effective SUSY transformation operator expandable in powers of the coupling constant g as delta = Sigma (n greater than or equa l to0)g(2n delta (n)), where delta ((0)) is of the tree-level form. Then, a part from an overall constant, the SUSY Ward identity delta Gamma = 0 deter mines the off-shell effective action Gamma uniquely to arbitrary order of p erturbation theory, provided that the SO(9) symmetry is preserved. Our proo f depends only on the properties of the tree-level SUSY transformation laws and does not require the detailed knowledge of quantum corrections. (C) 20 01 Elsevier Science B.V. All rights reserved.