Analysis of \mathbb{C}P^{N-1} sigma models via projective structures
Bibliographic record
Abstract
This paper represents a study of projector solutions to the Euclidean CP N -1 sigma model in two dimensions and their associated surfaces immersed in the su(N ) Lie algebra.Any solution for the CP N -1 sigma model defined on the extended complex plane with finite action can be written as a raising operator acting on a holomorphic one.Here the proof is formulated in terms rank-1 projectors so it is explicitly gauge invariant.We apply these results to the analysis of surfaces associated with the CP N -1 models defined using the generalized Weierstrass formula for immersion.We show that the surfaces are conformally parametrized by the Lagrangian density, with finite area equal to the action of the model, and express several other geometrical characteristics of the surface in terms of the physical quantities of the model.Finally, we provide necessary and sufficient conditions that a surface be related to a CP N -1 sigma model.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 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".