Emergence of spacetime in a restricted spin-foam model
Bibliographic record
Abstract
The spectral dimension has proven to be a very informative observable to understand the properties of quantum geometries in approaches to quantum gravity. In loop quantum gravity and its spin-foam description, it has not been possible so far to calculate the spectral dimension of spacetime. As a first step towards this goal, here we determine the spacetime spectral dimension in the simplified spin-foam model restricted to hypercuboids. Using Monte Carlo methods we compute the spectral dimension for state sums over periodic spin-foam configurations on infinite lattices. For given periodicity, i.e. number of degrees of freedom, we find a range of scale where an intermediate spectral dimension between 0 and 4 can be found, continuously depending on the parameter of the model. Under an assumption on the statistical behavior of the Laplacian we can explain these results analytically. This allows us to take the thermodynamic limit of large periodicity and find a phase transition from a regime of effectively zero-dimensional to four-dimensional spacetime. At the point of phase transition, dynamics of the model are scale invariant which can be seen as restoration of diffeomorphism invariance of flat space. Considering the spectral dimension as an order parameter for renormalization we find a renormalization group flow to this point as well. Being the first instance of an emergence of four-dimensional spacetime in a spin-foam model, the properties responsible for this result seem to be rather generic. We thus expect similar results for more general, less restricted spin-foam models.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".