Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral

Abstract

In this paper, we consider a reduced supersymmetric Yang-Mills integral with four supercharges by using a Gaussian approximation scheme and its improved version. We calculate the free energy and the expectation values of Polyakov 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 large $N$ limit leads simple formulas for the case of the loop length smaller. Also, 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 Wilson loop reproduces the result simulated for a few smaller values of $N$ at least qualitatively.

18 pages, 4 figures, LaTeX; comments added, the final version published in JHEP

References in corpus (4)

• Convergent Yang-Mills Matrix Theories
• Black hole entropy from non-perturbative gauge theory
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals

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