arXiv 0806.05582008-06hep-th

矩阵模型、规范理论与涌现几何

Matrix Models, Gauge Theory and Emergent Geometry

Rodrigo Delgadillo-Blando, Denjoe O'Connor, Badis Ydri

备注：: 41 pages,23 figures,two references added,typos corrected, extra comments included
发表信息：: JHEP 0905:049,2009
DOI：: 10.1088/1126-6708/2009/05/049

摘要：

我们提出，理论预测和蒙特卡罗模拟，一个简单的三矩阵模型，表现出一种奇异的相变。如果从高温侧或低温侧接近，转变的性质是非常不同的。高温相由三个自相互作用的随机矩阵描述，没有背景时空几何。当系统冷却时，有一个相变，其中经典的双球凝聚形成背景几何。该转变具有熵跃变或潜热，但比热随着从低温接近转变而发散。我们发现没有分歧或临界波动的证据时，过渡接近从高温相。在足够低的温度下，系统可以用耦合到大质量标量场的U（1）规范场在经典双球背景上的小涨落来描述。随着标量场质量的增加，临界温度被向上推。一旦几何相建立好，比热取1，规范场和标量场各贡献1/2。

英文摘要：

We present, theoretical predictions and Monte Carlo simulations, for a simple three matrix model that exhibits an exotic phase transition. The nature of the transition is very different if approached from the high or low temperature side. The high temperature phase is described by three self interacting random matrices with no background spacetime geometry. As the system cools there is a phase transition in which a classical two-sphere condenses to form the background geometry. The transition has an entropy jump or latent heat, yet the specific heat diverges as the transition is approached from low temperatures. We find no divergence or evidence of critical fluctuations when the transition is approached from the high temperature phase. At sufficiently low temperatures the system is described by small fluctuations, on a background classical two-sphere, of a U(1) gauge field coupled to a massive scalar field. The critical temperature is pushed upwards as the scalar field mass is increased. Once the geometrical phase is well established the specific heat takes the value 1 with the gauge and scalar fields each contributing 1/2.

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英文摘要：

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