A theorem on the power of supersymmetry in Matrix theory Original Research Article

For the so-called source-probe configuration in Matrix theory, we prove the following theorem concerning the power of supersymmetry (SUSY): let δ be a quantum-corrected effective SUSY transformation operator expandable in powers of the coupling constant g as δ=∑n⩾0g2nδ(n), where δ(0) is of the tree-level form. Then, apart from an overall constant, the SUSY Ward identity δΓ=0 determines the off-shell effective action Γ uniquely to arbitrary order of perturbation theory, provided that the SO(9) symmetry is preserved. Our proof depends only on the properties of the tree-level SUSY transformation laws and does not require the detailed knowledge of quantum corrections.