High Energy Physics - Theory · arXiv:hep-th/0202149 v2 · submitted 21 Feb 2002
Hyperkahler Cones and Orthogonal Wolf Spaces
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“Finally, using a representation of the hyperkahler quotient via quiver diagrams, we deduce the existence of a new eight dimensional ALE space.”
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Abstract
We construct the hyperkahler cones corresponding to the Quaternion-Kahler orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions, which appear in hypermultiplet couplings to N=2 supergravity. The geometry is completely encoded by a single function, the hyperkahler potential, which we compute from an SU(2) hyperkahler quotient of flat space. We derive the Killing vectors and moment maps for the SO(n+4) isometry group on the hyperkahler cone. For the non-compact case, the isometry group SO(n,4) contains n+2 abelian isometries which can be used to find a dual description in terms of n tensor multiplets and one double-tensor multiplet. Finally, using a representation of the hyperkahler quotient via quiver diagrams, we deduce the existence of a new eight dimensional ALE space.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.99
What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.47 · compares with prior results 0.06 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We construct the hyperkahler cones corresponding to the Quaternion-Kahler orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions, which appear in hypermultiplet couplings to N=2 supergravity. | contribution 1.00 | 0.94 | 0.37 | asserted 1.00 |
| The geometry is completely encoded by a single function, the hyperkahler potential, which we compute from an SU(2) hyperkahler quotient of flat space. | method 0.78 | 0.92 | 0.12 | asserted 1.00 |
| We derive the Killing vectors and moment maps for the SO(n+4) isometry group on the hyperkahler cone. | contribution 0.59 | 0.95 | 0.08 | asserted 1.00 |
| For the non-compact case, the isometry group SO(n,4) contains n+2 abelian isometries which can be used to find a dual description in terms of n tensor multiplets and one double-tensor multiplet. | result 0.87 | 0.78 | 0.12 | asserted 0.86 |
| Finally, using a representation of the hyperkahler quotient via quiver diagrams, we deduce the existence of a new eight dimensional ALE space. | result 0.92 | 0.94 | 0.32 | asserted 0.99 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
What was examined, and what was not
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- arXiv listing abstract v2
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,411 input tokens, $0.0002 reported.
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Reviewed papers on Pith that cite this one. The full citation record
- String loop corrected hypermultiplet moduli spaces hep-th · Feb 2006
How the literature uses it
2 arXiv papers cite this in 5 sentences
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Compares with it 1 paper
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By comparing our calculations with those in [ref] , one easily sees that [ref], [ref] and [ref] are just the conditions to set all nine moment maps of the $SU(2)$ generated by $su_2(2)$ to zero.
Type II compactifications on manifolds with SU(2) x SU(2) structure · The hyperkähler cone · 1.00
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