Supersymmetric completion of supersymmetric quantum mechanics

Via supersymmetry argument, we determine the effective action of the SU(2) supersymmetric Yang-Mills quantum mechanics up to two constants, which results from the full supersymmetric completion of the F⁴ term. The effective action, consisting of zero, two, four, six and eight fermion terms, agrees with the known perturbative one-loop calculations from the type II string theory and the matrix theory. Our derivation thus demonstrates its non-renormalization properties, namely, the one-loop exactness of the aforementioned action and the absence of the non-perturbative corrections. We briefly discuss generalizations to other branes and the comparison to the DLCQ supergravity analysis. In particular, our results show that the stringent constraints from the supersymmetry are responsible for the agreement between the matrix theory and supergravity with sixteen supercharges.