The gaugino condensate from asymmetric four-torus with twists
Bibliographic record
Abstract
A bstract We calculate the gaugino condensate in SU(2) super Yang-Mills theory on an asymmetric four-torus 𝕋 4 with ’t Hooft’s twisted boundary conditions. The 𝕋 4 asymmetry is controlled by a dimensionless detuning parameter ∆, proportional to L 3 L 4 − L 1 L 2 , with L i denoting the 𝕋 4 periods. We perform our calculations via a path integral on a 𝕋 4 . Its size is taken much smaller than the inverse strong scale Λ and the theory is well inside the semi-classical weak-coupling regime. The instanton background, constructed for ∆ ≪ 1 in [1], has fractional topological charge $$ Q=\frac{1}{2} $$ Q = 1 2 and supports two gaugino zero modes, yielding a non-vanishing bilinear condensate, which we find to be ∆-independent. Further, the theory has a mixed discrete chiral/1-form center anomaly leading to double degeneracy of the energy eigenstates on any size torus with ’t Hooft twists. In particular, there are two vacua, ∣0〉 and ∣1〉, that are exchanged under chiral transformation. Using this information, the ∆-independence of the condensate, and assuming further that the semi-classical theory is continuously connected to the strongly-coupled large-𝕋 4 regime, we determine the numerical coefficient of the gaugino condensate: 〈0|trλλ|0〉 = ∣〈1|trλλ|1〉∣ = 32π 2 Λ 3 , a result equal to twice the known ℝ 4 value. We discuss possible loopholes in the continuity approach that may lead to this discrepancy.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".