Gaussian and mean field approximations for reduced 4D supersymmetric Yang-Mills integral

In this paper, we consider a reduced supersymmetric Yang-Mills integral wit h four supercharges by using a gaussian approximation scheme and its improv ed version. We calculate the free energy and the expectation values of Poly akov loop and Wilson loop operators by extending the method employed in the bosonic case in the previous paper. Our results nicely match to the exact and the numerical results obtained before. The loop amplitudes exhibit good scaling behaviors similarly as in the bosonic case. The 't Hooft like larg e N limit leads simple formulas for the case of the loop length smaller. Al so, the Polyakov loop and the Wilson loop are computed for the case of the loop length sufficiently large, where we see that the behavior of the Wilso n loop reproduces the result simulated for a few smaller values of N at lea st qualitatively.