用矩阵模型鞍点形成BPS态
Shaping up BPS States with Matrix Model Saddle Points
摘要：
我们提供了一个量子力学模型的交换矩阵在大N极限的一个家庭的波函数的概率分布的分析结果。这些波函数描述了N=4超对称Yang-Mills理论1/8BPS态的强耦合极限。因此，在大N极限下，它们应该是渐近接近AdS 5xS 5的IIB型超引力经典解的对偶。每个概率分布可以描述为一个矩阵模型的配分函数（不同的波函数对应于不同的矩阵模型势），我们通过鞍点近似研究。这些鞍点的解决方案给出的（五维）超曲面支持密度分布的特征值。
英文摘要：
We provide analytical results for the probability distribution of a family of wavefunctions of a quantum mechanics model of commuting matrices in the large-N limit. These wavefunctions describe the strong coupling limit of 1/8 BPS states of N=4 supersymmetric Yang-Mills theory. Therefore, in the large-N limit, they should be dual to classical solutions of type IIB supergravity that asymptotically approach AdS5xS5. Each probability distribution can be described as the partition function of a matrix model (different wavefunctions correspond to different matrix model potentials) which we study by means of a saddle point approximation. These saddle point solutions are given in terms of (five-dimensional) hypersurfaces supporting density distributions of eigenvalues.
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