  We study the quantum mechanical sigma model arising in the discrete
light-cone quantisation of N=4 supersymmetric Yang-Mills theory. The target
space is a certain torus fibration over a scale-invariant special Kahler
manifold. We show that the expected SU(1,1|4) light-cone superconformal
invariance of the N=4 theory emerges in a limit where the volume of the fibre
goes to zero and give an explicit construction of the generators. The
construction given here yields a large new family of superconformal quantum
mechanical models with SU(1,1|4) invariance.
