Excitations in the higher-lattice gauge theory model for topological phases. I. Overview
Bibliographic record
Abstract
In this series of papers, we study a Hamiltonian model for (3+1)-dimensional topological phases introduced in [Bullivant et al., Phys. Rev. B 95, 155118 (2017)], based on a generalization of lattice gauge theory known as ``higher-lattice gauge theory.'' Higher-lattice gauge theory has so-called ``2-gauge fields'' describing the parallel transport of lines, in addition to ordinary 1-gauge fields which describe the parallel transport of points. In this series we explicitly construct the creation operators for the pointlike and looplike excitations supported by the model. We use these creation operators to examine the properties of the excitations, including their braiding statistics. These creation operators also reveal that some of the excitations are confined, costing energy to separate that grows linearly with the length of the creation operator used. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to rederive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground-state degeneracy on the 3-torus is related to the number of types of linked looplike excitations. This first paper provides an accessible summary of our findings, with more detailed results and proofs to be presented in the other papers in the series.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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 teacher head, 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".