Abelianization of BPS quivers and the refined Higgs index
Bibliographic record
Abstract
We count Higgs “phase” BPS states of general non-Abelian quiver, possibly with loops, by mapping the problem to its Abelian, or toric, counterpart and imposing Weyl invariance later. Precise Higgs index computation is particularly important for quivers with superpotentials; the Coulomb “phase” index is recently shown to miss important BPS states, dubbed intrinsic Higgs states or quiver invariants. We demonstrate how the refined Higgs index is naturally decomposed to a sum over partitions of the charge. We conjecture, and show in simple cases, that this decomposition expresses the Higgs index as a sum over a set of partition-induced Abelian quivers of the same total charge but generically of smaller rank. Unlike the previous approach inspired by a similar decomposition of the Coulomb index, our formulae compute the quiver invariants directly, and thus offer a self-complete routine for counting BPS states.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| 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".