Bibliographic record
Abstract
Abstract We present here a careful study of the holographic duals of BPS surface operators in the 6d <?CDATA ${\cal N} = (2,0)$?> theory. Several different classes of surface operators have been recently identified and each class has a specific calibration form—a 3-form in <?CDATA $AdS_7\times S^4$?> A d S 7 × S 4 whose pullback to the M2-brane world-volume is equal to the volume form. In all but one class, the appropriate forms are exact, so the action of the M2-brane is easily expressed in terms of boundary data, which is the geometry of the surface. Specifically, for surfaces of vanishing anomaly, it is proportional to the integral of the square of the extrinsic curvature. This can be extended to the case of surfaces with anomalies, by taking the ratio of two surfaces with the same anomaly. This gives a slew of new expectation values at large N in this theory. For one specific class of surface operators, which are Lagrangian submanifolds of <?CDATA ${\mathbb R}^4\subset {\mathbb R}^6$?> R 4 ⊂ R 6 , the structure is far richer and we find that the M2-branes are special Lagrangian submanifold of an appropriate six-dimensional almost Calabi-Yau submanifold of <?CDATA $AdS_7\times S^4$?> A d S 7 × S 4 . This allows for an elegant treatment of many such examples.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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".