Kazhdan‐Lusztig correspondence for vertex operator superalgebras from abelian gauge theories
Bibliographic record
Abstract
Abstract We prove the Kazhdan–Lusztig correspondence for a class of vertex operator superalgebras that, via the work of Costello–Gaiotto, arise as boundary vertex operator algebra (VOAs) of the topological B twist of 3d abelian gauge theories. This means that we show equivalences of braided tensor categories of modules of certain affine vertex superalgebras and corresponding quantum supergroups. We build on the work of Creutzig–Lentner–Rupert for this large class of VOAs and extend it since, in our case, the categories do not have projective objects, and objects can have arbitrary Jordan–Hölder length. Our correspondence significantly improves the understanding of the braided tensor category of line defects associated with this class of topological quantum field theory (TQFT) by realizing line defects as modules of a Hopf algebra. In the process, we prove a special case of the conjecture of Semikhatov–Tipunin, relating logarithmic conformal field theory (CFTs) to Nichols algebras of screening operators.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".