The Virasoro Algebra: Signatures of Highest Weight Modules and the Modular Group Action
Bibliographic record
Abstract
The Virasoro algebra (\\emph{Vir}) has important applications to the study of infinite dimensional Lie algebras, and specifically to areas of theoretical physics modeled by conformal field theories. The positive-energy representations of \\emph{Vir} play a key role in string theory. A vital piece of information is the signature of the positive-energy representations. The physicist Adrian Kent calculated the characters of the signatures of these positive-energy representations in his paper. In this thesis, we will provide mathematical proofs for Kent's signature formulas for all possible values of the central charge and lowest weight. Furthermore, we simplify Kent's formulas by adopting a different approach to viewing the formulas. An important consequence is a clean reformulation in the minimal model case, which is of tremendous interest to theoretical physicists who wish to understand the modular group action in order to apply Kent's formulas to the study of non-unitary conformal field theories. We discuss how to compute the modular group action.
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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 | 0.003 |
| 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 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".