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 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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".