Gravitational Blocks, Spindles and GK Geometry
Bibliographic record
Abstract
Abstract We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> solutions of $$D=11$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> </mml:math> supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell c -function in the dual field theory, establishing a very general exact result in holography. For the AdS $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS $$_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msub> </mml:math> .
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".