New critical behavior in a supersymmetric double-well matrix model
New critical behavior in a supersymmetric double-well matrix model
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超对称双阱矩阵模型中的新临界行为
DOI：
10.1016/j.nuclphysb.2012.09.020
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Tsunehide Kuroki and Fumihiko Sugino
中科院分区：
文献类型：
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作者：
山田泰一;船木靖郎;明孝之;堀内昶;池田清美;G. Ropke;P. Schuck;東崎昭弘;Tsunehide Kuroki and Fumihiko Sugino
在一个简单的超对称矩阵模型中，我们在平面水平上计算了各种关联函数，该模型的标量势为双势垒型。该模型通过填充分数ν±来参数化无限简并真空，该分数表示双势垒两个极小值周围的矩阵本征值的个数。计算的一般填充分数对应于本征值分布的一般二次解。该模型被映射到n=−2的随机表面上的O(N)模型，模型的某些扇区用具有c=−2物质或(2，1)极小弦理论的二维量子引力来描述.对于不可能进行这种描述的另一个扇区，我们发现了相关函数对数次方的新的临界行为。我们将矩阵模型看作Penner模型的超对称模拟，并从对称性和谱的角度讨论了矩阵模型与二维IIA型超弦理论的对应关系。特别地，矩阵模型中的单迹算子被自然地解释为IIA型理论中的顶点算子。关联函数的结果还表明，对应的IIA型理论具有非平凡的Ramond-Ramond背景。
We compute various correlation functions at the planar level in a simple supersymmetric matrix model, whose scalar potential is in shape of a double-well. The model has infinitely degenerate vacua parametrized by filling fractions ν±representing the numbers of matrix eigenvalues around the two minima of the double-well. The computation is done for general filling fractions corresponding to general two-cut solutions for the eigenvalue distribution. The model is mapped to the O(n) model on a random surface with n=−2, and some sector of the model is described by two-dimensional quantum gravity with c=−2 matter or (2,1) minimal string theory. For the other sector in which such description is not possible, we find new critical behavior of powers of logarithm for correlation functions. We regard the matrix model as a supersymmetric analog of the Penner model, and discuss correspondence of the matrix model to two-dimensional type IIA superstring theory from the viewpoint of symmetry and spectrum. In particular, single-trace operators in the matrix model are naturally interpreted as vertex operators in the type IIA theory. Also, the result of the correlation functions implies that the corresponding type IIA theory has a nontrivial Ramond–Ramond background.