Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
复制标题
简化 4D 超对称 Yang-Mills 积分的高斯和平均场近似
DOI：
10.1088/1126-6708/2001/07/014
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Fumihiko Sugino
中科院分区：
文献类型：
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作者：
Fumihiko Sugino
本文利用高斯近似格式及其改进版本，研究了具有四个增压的简化超对称Yang-Mills积分。我们通过推广前一篇文章中玻色子情况下所采用的方法，计算了Polyakov环和Wilson环算子的自由能和期望值。我们的计算结果与以前的精确和数值计算结果吻合得很好。环路振幅表现出与玻色子情况类似的良好标度行为。‘t ’ Hooft像大$N$的限制导致循环长度较小的情况下的简单公式。此外，在循环长度足够大的情况下，对Polyakov循环和Wilson循环进行了计算，在这种情况下，我们看到Wilson循环的行为至少在定性上再现了几个较小的N值所模拟的结果。
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.