Bibliographic record
Abstract
Conformal field theory: the physics of MoonshineThis chapter presents the physical context for Moonshine.Rather than diving into a conventional discourse of conformal field theory (CFT), it might be more helpful to take several steps back and begin with Galileo.Physics even more than mathematics is interwoven with history.Our treatment of CFT is sketchy but should supply the reader with all that is necessary to appreciate the absolutely profound role physics has played in Moonshine and other aspects of 'pure' mathematics in recent years.It is hoped that this chapter will make it easier for the interested reader to pursue more standard treatments of CFT and string theory.It is written primarily with the mathematician in mind.The third section explores the physics of CFT, and the fourth describes some mathematical formulations.CFT is to a generic quantum field theory what finite-dimensional semi-simple Lie algebras are to generic Lie algebras.Background for both sections is provided by the review of classical and quantum physics sketched in the first two sections.For a mathematician studying physics, important to keep in mind is that physics has been driven historically more by its predictive power than by conceptual concerns (with a few remarkable exceptions, such as Einstein's general relativity).Given enough time, however, the theory becomes polished to a state of pristine mathematical elegance, as classical mechanics amply demonstrates.In particular, one has the sense that quantum theory is ad hoc and rather unsound -and it is both -but these features are due to the historical accident that we were born too close to its inception.Much more important is what it can teach mathematics, which is considerable.The essence of quantum field theory is completely accessible to mathematicians and, as mathematics of the late twentieth century shows, should at least in its broad strokes be part of their standard repertoire.A special feature of classical physics is that the behaviour of a system -for example, its trajectory in phase space -becomes much simpler when looked at infinitesimally.The simple universal regularities are captured by differential equations; the complicated incidental features of a specific situation are relegated to the initial conditions.Among mathematicians, this central role of partial differential equations in classical physics was responsible for what had been a near-identification of their study with the subject they call mathematical physics.It was largely with the arrival of string theory that a much richer range of mathematics became relevant to physics, and it is this happy development that made this book possible.Almost every facet of Moonshine fits comfortably into CFT, where it often was discovered first.Some have questioned though the necessity of involving such a complicated
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.021 | 0.003 |
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".