Bibliographic record
Abstract
Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m) × O(n) global symmetry in d = 3 spacetime dimensions.We use both analytic and numerical bootstrap techniques.Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in ε = 4 -d and in 1/n, with a method that generalizes to arbitrary global symmetry.Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature.Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2) × O(n) theories for various values of n.Some of these islands can be attributed to fixed points predicted by perturbative methods like the ε and large-n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.005 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.911 | 0.884 |
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".