Emergent gravity in two dimensions |
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Authors: | D. Sexty C. Wetterich |
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Affiliation: | Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany |
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Abstract: | 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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Keywords: | Numerical gravity Self-tuned criticality Lattice diffeomorphism invariance |
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