Fibred GK geometry and supersymmetric AdS solutions
Bibliographic record
Abstract
A bstract We continue our study of a general class of $$ \mathcal{N}=2 $$ N = 2 supersymmetric AdS 3 × Y 7 and AdS 2 × Y 9 solutions of type IIB and D = 11 supergravity, respectively. The geometry of the internal spaces is part of a general family of “GK geometries”, Y 2 n +1 , n ≥ 3, and here we study examples in which Y 2 n +1 fibres over a Kähler base manifold B 2 k , with toric fibres. We show that the flux quantization conditions, and an action function that determines the supersymmetric R -symmetry Killing vector of a geometry, may all be written in terms of the “master volume” of the fibre, together with certain global data associated with the Kähler base. In particular, this allows one to compute the central charge and entropy of the holographically dual (0 , 2) SCFT and dual superconformal quantum mechanics, respectively, without knowing the explicit form of the Y 7 or Y 9 geometry. We illustrate with a number of examples, finding agreement with explicit supergravity solutions in cases where these are known, and we also obtain new results. In addition we present, en passant , new formulae for calculating the volumes of Sasaki-Einstein manifolds.
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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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".