The hexagon in the mirror: the three-point function in the SoV representation
Bibliographic record
Abstract
We derive an integral expression for the leading-order type I–I–I three-point functions in the su ( 2 ) -sector of N = 4 super Yang–Mills theory, for which no determinant formula is known. To this end, we first map the problem to the partition function of the six vertex model with a hexagonal boundary. The advantage of the six-vertex model expression is that it reveals an extra symmetry of the problem, which is the invariance under 90° rotation. On the spin-chain side, this corresponds to the exchange of the quantum space and the auxiliary space and is reminiscent of the mirror transformation employed in the worldsheet S -matrix approaches. After the rotation, we then apply Sklyanin’s separation of variables (SoVs) and obtain a multiple-integral expression of the three-point function. The resulting integrand is expressed in terms of the so-called Baxter polynomials, which is closely related to the quantum spectral curve approach. Along the way, we also derive several new results about the SoV, such as the explicit construction of the basis with twisted boundary conditions and the overlap between the orginal SoV state and the SoV states on the subchains.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".