Invariant Yang-Mills connections over non-reductive pseudo-Riemannian homogeneous spaces
Bibliographic record
Abstract
We study invariant gauge fields over the 4-dimensional non-reductive pseudo-Riemannian homogeneous spaces G / K G/K recently classified by Fels and Renner (2006). Given H H compact semi-simple, classification results are obtained for principal H H -bundles over G / K G/K admitting: (1) a G G -action (by bundle automorphisms) projecting to left multiplication on the base, and (2) at least one G G -invariant connection. There are two cases which admit non-trivial examples of such bundles, and all G G -invariant connections on these bundles are Yang–Mills. The validity of the principle of symmetric criticality (PSC) is investigated in the context of the bundle of connections and is shown to fail for all but one of the Fels–Renner cases. This failure arises from degeneracy of the scalar product on pseudo-tensorial forms restricted to the space of symmetric variations of an invariant connection. In the exceptional case where PSC is valid, there is a unique G G -invariant connection which is moreover universal; i.e., it is the solution of the Euler–Lagrange equations associated to any G G -invariant Lagrangian on the bundle of connections. This solution is a canonical connection associated with a weaker notion of reductivity which we introduce.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".