Entropic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> function of three-dimensional Ising conformal field theory via fuzzy sphere regularization
Bibliographic record
Abstract
The $F$ function, the three-dimensional counterpart of the central charge in the two-dimensional (2D) conformal field theory, measures the effective number of degrees of freedom in three-dimensional (3D) quantum field theory, and it is monotonically decreasing under the renormalization group flow. However, unlike the 2D central charge, the $F$ function is a nonlocal quantity and cannot be computed using correlators of local operators. Utilizing the recently proposed fuzzy sphere regularization, we have performed the first nonperturbative computation of the $F$ function for the paradigmatic 3D Ising conformal field theory through entanglement entropy. Our computation yields ${F}_{\text{Ising}}=0.0612(5)$, slightly smaller than the $F$ function of a real free scalar, ${F}_{\text{free}}=\frac{log2}{8}\ensuremath{-}\frac{3\ensuremath{\zeta}(3)}{16{\ensuremath{\pi}}^{2}}\ensuremath{\approx}0.0638$, consistent with the $F$ theorem, and close to the $4\ensuremath{-}\ensuremath{\epsilon}$ expansion estimates of ${F}_{\text{Ising}}\ensuremath{\approx}0.061\ensuremath{\sim}0.062$.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".