Toric geometry and the dual of ℐ-extremization
Bibliographic record
Abstract
Abstract We consider d = 3, $$ \mathcal{N}=2 $$ N = 2 gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, Σ g , with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a D = 11 supergravity dual of the form AdS2 × Y 9, with electric four-form flux and where Y 9 is topologically a fibration of a Sasakian Y 7 over Σ g . These D = 11 solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS4 × Y 7, with a Sasaki-Einstein metric on Y 7. We show that an off-shell entropy function for the dual AdS2 solutions may be computed using the toric data and Kähler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of Y 7 over Σ g and a Kähler class parameter for Σ g . We also discuss the class of supersymmetric AdS3 × Y 7 solutions of type IIB supergravity with five-form flux only in the case that Y 7 is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning ℐ-extremization.
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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) | 0.000 | 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 | 0.001 |
| 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".