Effective Superpotentials, Geometry and Integrable Systems
Bibliographic record
Abstract
We consider the effective superpotentials of N = 1 SU(N c ) and U(N c ) supersymmetric gauge theories that are obtained from the N = 2 theory by adding a tree-level superpotential.We show that several of the techniques for computing the effective superpotential are implicitly regularized by 2N c massive chiral multiplets in the fundamental representation, i.e the gauge theory is embedded in the finite theory with nontrivial UV fixed point.In the maximally confining phase we obtain explicit general formulae for the effective superpotential, which reduce to previously known results in particular cases.In order to study N = 1 and N = 2 theories with fundamentals, we explicitly factorize the Seiberg-Witten curve for 0 ≤ N f < 2N c and use the results to rederive the N = 1 superpotential.N = 2 gauge theories have an underlying integrable structure, and we obtain results on a new Lax matrix for N f = N c .
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".