  We study supersymmetric quantum mechanics on the moduli space of Yang-Mills
instantons on R^2 x T^2 and its application to the discrete light-cone
quantisation (DLCQ) of N=4 SUSY Yang-Mills. In the presence of a target space
magnetic field, the model has a discrete spectrum with the wavefunctions of
generic energy eigenstates supported away from the singular points of the
moduli space. The corresponding Hamiltonian is part of an osp(1,1|4)
superalgebra which enlarges to su(1,1|4) superconformal invariance in the
sector corresponding to the N=4 theory. The Hamiltonian is isospectral to the
light-cone dilatation operator of the N=4 theory in this sector. The model also
has an interesting scaling limit where it becomes integrable. We determine the
semiclassical spectrum in this limit. We discuss a possible approach to
constructing the dilatation operator of N=4 supersymmetric Yang-Mills theory in
DLCQ.
