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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.