Logarithmic $M \left( 2,p \right)$ Minimal Models, their Logarithmic Couplings, and Duality.
Bibliographic record
Abstract
A natural construction of the logarithmic extension of the M (2, p) minimal models is presented, which generalises our previous model [1] of percolation (p = 3).Its key aspect is the replacement of the minimal model irreducible modules by reducible ones obtained by requiring that only one of the two principal singular vectors of each module vanish.The resulting theory is then constructed systematically by repeatedly fusing these building block representations.This generates indecomposable representations of the type which signify the presence of logarithmic partner fields in the theory.The basic data characterising these indecomposable modules, the logarithmic couplings, are computed for many special cases and given a new structural interpretation.Quite remarkably, a number of them are presented in closed analytic form (for general p).These are the prime examples of "gauge-invariant" data -quantities independent of the ambiguities present in defining the logarithmic partner fields.Finally, mere global conformal invariance is shown to enforce strong constraints on the allowed spectrum: It is not possible to include modules other than those generated by the fusion of the model's building blocks.This generalises the statement that there cannot exist two effective central charges in a c = 0 model.It also suggests the existence of a second "dual" logarithmic theory for each p.Such dual models are briefly discussed.December 3, 2007
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".