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arXiv 1208.2168hep-thcond-mat.stat-mechgr-qchep-lat
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二维中的突现引力

Emergent gravity in two dimensions

D. Sexty, C. Wetterich

摘要:

我们通过数值模拟的方法探索了具有突现引力和度量的模型。一种特殊类型的二维非线性西格玛模型的正则化和离散化的二次格。它的特点是格点同态不变性,保证了一般坐标变换在连续极限的对称性。我们观察到一个集体的序参量与度量的性质,显示Minkowski或欧几里得签名。度规的关联函数揭示了一个有趣的长距离行为,具有类似幂的衰减。这种普遍的临界行为在没有调整参数的情况下发生,因此构成了这种类型的西格玛模型的“自调整临界性”的例子。我们还发现了一个非零的期望值的“zweibein”有关的“内部”自由度的标量场,再次与远程相关。该指标被很好地描述为zweibein的合成物。纯量凝聚破坏了欧几里德旋转对称性。

英文摘要:

We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice diffeomorphism invariance which ensures in the continuum limit the symmetry of general coordinate transformations. We observe a collective order parameter with properties of a metric, showing Minkowski or euclidean signature. The correlation functions of the metric reveal an interesting long-distance behavior with power-like decay. This universal critical behavior occurs without tuning of parameters and thus constitutes an example of "self-tuned criticality" for this type of sigma-models. We also find a non-vanishing expectation value of a "zweibein" related to the "internal" degrees of freedom of the scalar field, again with long-range correlations. The metric is well described as a composite of the zweibein. A scalar condensate breaks euclidean rotation symmetry.

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