Fractional-Level Kac-Moody Algebras and Nonunitary Coset Conformal Theories
Bibliographic record
Abstract
In the coset construction, the admissible representations of Kaö-Moody algebras at fractional level give rise to nonunitary conformal field theories. We simplify the description (due to Kač and Wakimoto) of the possible highest weights of admissible representations. For every subgroup of the centre of a finite Lie algebra, we find an infinite sequence of modular invariant combinations of characters of admissible representations. Products of our invariants provide a large class of partition functions (and therefore the spectra) of nonunitary coset models. Under an assumption (proved valid for su(2) and su(3)) we give a formula for the fusion rules of untwisted affine algebras at fractional level, in terms of those at integer level and the affine outer automorphisms. We also find a more general formula expressing them in terms of the affine Weyl group and integer-level fusion rules. These formulae determine the fusion rules for nonunitary coset models. Finally, a suggestive linear relation is found between the modular 5 matrices for the fractional level algebras and those for the corresponding (nonunitary) WN minimal models.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.003 | 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".