  We study a non-perturbative formulation of N=4 super Yang-Mills theory (SYM)
on RxS^3 proposed in arXiv:0807.2352. This formulation is based on the large-N
reduction, and the theory can be described as a particular large-N limit of the
plane wave matrix model (PWMM), which is obtained by dimensionally reducing the
original theory over S^3. In this paper, we perform some tests for this
proposal. We construct an operator in the PWMM that corresponds to the Wilson
loop in SYM in the continuum limit and calculate the vacuum expectation value
of the operator for the case of the circular contour. We find that our result
indeed agrees with the well-known result first obtained by Erickson, Semenoff
and Zarembo. We also compute the beta function at the 1-loop level based on
this formulation and see that it is indeed vanishing.
