We investigate the large N reduced model of gauge theory on a curved
spacetime through the plane wave matrix model. We formally derive the action of
the N=4 supersymmetric Yang-Mills theory on R \times S^3 from the plane wave
matrix model in the large N limit. Furthermore, we evaluate the effective
action of the plane wave matrix model up to the two-loop level at finite
temperature. We find that the effective action is consistent with the free
energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature
limit where the planar contributions dominate. We conclude that the plane wave
matrix model can be used as a large N reduced model to investigate
nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \times
S^3.Comment: 31pages: added comments and reference
