Mass-deformed super Yang-Mills theory on $$ {\mathbbm{T}}^4 $$: sum over twisted sectors, θ-angle, and CP violation
Bibliographic record
Abstract
A bstract We study SU( N ) super Yang-Mills theory with a small gaugino mass m and vacuum angle θ on the four-torus $$ {\mathbbm{T}}^4 $$ T 4 with ’t Hooft twisted boundary conditions. Introducing a detuning parameter ∆, which measures the deviation from an exactly self-dual $$ {\mathbbm{T}}^4 $$ T 4 , and working in the limits mLN ≪ Λ LN ≪ 1 and $$ \frac{\left(N-1\right){m}^2{L}^2}{4\pi}\ll \Delta \ll 1 $$ N − 1 m 2 L 2 4 π ≪ ∆ ≪ 1 , where L is the torus size and Λ the strong-coupling scale, we compute the scalar and pseudo-scalar condensates to leading order in m 2 L 2 /∆. The twists generate fractional-charge instantons, and we show that summing over all such contributions is crucial for reproducing the correct physical observables in the decompactified strong-coupling regime. From a Hamiltonian perspective, the sum over twisted sectors, already at small torus size, projects in the m = 0 limit onto a definite superselection sector of the ℝ 4 theory. In the massless limit, we recover the exact value of the gaugino condensate |〈 λλ 〉| = 16 π 2 Λ 3 , and demonstrate how a spurious U(1) symmetry eliminates all $$ \mathcal{CP} $$ CP -violating effects. Our results are directly testable in lattice simulations, and our method extends naturally to non-supersymmetric gauge theories.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".