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 resu lts from the full supersymmetric completion of the F-4 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 t heory and the matrix theory. Our derivation thus demonstrates its non-renor malization properties, namely, the one-loop erectness of the aforementioned action and the absence of the non-perturbative corrections. We briefly dis cuss generalizations to other branes and the comparison to the DLCQ supergr avity analysis. In particular, our results show that the stringent constrai nts from the supersymmetry are responsible for the agreement between the ma trix theory and supergravity with sixteen supercharges. (C) 1999 Elsevier S cience B.V. All rights reserved.