Holomorphic bundles and the moduli space of N=1 supersymmetric heterotic compactifications
Bibliographic record
Abstract
We describe the first order moduli space of heterotic string theory compactifications which preserve N =1 supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we promote a connection on T X to a field, the moduli space corresponds to deformations of a holomorphic structure $$ \overline{D} $$ on a bundle $$ \mathcal{Q} $$ . The bundle $$ \mathcal{Q} $$ is constructed as an extension by the cotangent bundle T ∗ X of the bundle E = End(V )⊕End(TX)⊕TX with an extension class $$ \mathcal{H} $$ which precisely enforces the anomaly cancelation condition. The deformations corresponding to the bundle E are simultaneous deformations of the holomorphic structures on the poly-stable bundles V and T X together with those of the complex structure of X. We discuss the fact that the “moduli” corresponding to End(T X) cannot be physical, but are however needed in our mathematical structure to be able to enforce the anomaly cancelation condition. In the appendix we comment on the choice of connection on T X which has caused some confusion in the community before. It has been shown by Ivanov and others that this connection should also satisfy the instanton equations, and we give another proof of this fact.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 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".