Emergent gravity in two dimensions

Authors/Editors

Research Areas

Publication Details

Output type: Journal article

Author list: Sexty D, Wetterich C

Publisher: Elsevier

Publication year: 2013

Journal: Nuclear Physics B (0550-3213)

Volume number: 867

Issue number: 2

Start page: 290

End page: 329

Number of pages: 40

ISSN: 0550-3213

eISSN: 1873-1562

Languages: English-Great Britain (EN-GB)

Unpaywall Data

Open access status: green

Full text URL: https://arxiv.org/pdf/1208.2168

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. (C) 2012 Elsevier B.V. All rights reserved.

Keywords

Lattice diffeomorphism invariance, Numerical gravity, Self-tuned criticality

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