Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases
Bibliographic record
Abstract
We study the quantized topological terms in a weak-coupling gauge theory with gauge group ${G}_{g}$ and a global symmetry ${G}_{s}$ in $d$ space-time dimensions. We show that the quantized topological terms are classified by a pair $(G,{\ensuremath{\nu}}_{d})$, where $G$ is an extension of ${G}_{s}$ by ${G}_{g}$ and ${\ensuremath{\nu}}_{d}$ an element in group cohomology ${\mathcal{H}}^{d}(G,\mathbb{R}/\mathbb{Z})$. When $d=3$ and/or when ${G}_{g}$ is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (i.e., gapped long-range-entangled phases with symmetry). Thus, those SET phases are classified by ${\mathcal{H}}^{d}(G,\mathbb{R}/\mathbb{Z})$, where $G/{G}_{g}={G}_{s}$. We also apply our theory to a simple case ${G}_{s}={G}_{g}={Z}_{2}$, which leads to 12 different SET phases in $2+1$ dimensions [(2+1)D], where quasiparticles have different patterns of fractional ${G}_{s}={Z}_{2}$ quantum numbers and fractional statistics. If the weak-coupling gauge theories are gapless, then the different quantized topological terms may describe different gapless phases of the gauge theories with a symmetry ${G}_{s}$, which may lead to different fractionalizations of ${G}_{s}$ quantum numbers and different fractional statistics [if in ($2+1$)D].
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".