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Topics in Cubic Special Geometry
High Energy Physics - Theory · Submitted 2 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions.
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We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbits, which we classify in some detail within the "special coordinates" symplectic frame. Finally, after a brief account of the action of PQ transformations on the recently established correspondence between Cayley's hyperdeterminant and elliptic curves, we derive an equivalent, alternative expression of I4, with relevant application to black hole entropy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. | contribution 0.65 | 0.76 | 0.05 | asserted 0.55 |
| s1 | Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. | result 0.67 | 0.73 | 0.29 | asserted 0.89 |
| s2 | Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. | result 0.83 | 0.49 | 0.13 | asserted 0.87 |
| s3 | This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. | interpretation 0.84 | 0.59 | 0.26 | hedged possibility 0.82 |
| s4 | Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbits, which we classify in some detail within the "special coordinates" symplectic frame. | result 0.81 | 0.85 | 0.21 | asserted 0.62 |
| s5 | Finally, after a brief account of the action of PQ transformations on the recently established correspondence between Cayley's hyperdeterminant and elliptic curves, we derive an equivalent, alternative expression of I4, with relevant application to black hole entropy. | result 0.64 | 0.91 | 0.19 | asserted 1.00 |
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Original abstract
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbits, which we classify in some detail within the "special coordinates" symplectic frame. Finally, after a brief account of the action of PQ transformations on the recently established correspondence between Cayley's hyperdeterminant and elliptic curves, we derive an equivalent, alternative expression of I4, with relevant application to black hole entropy.
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8 arXiv papers cite this in 11 sentences
Papers citing it · 9 sentences without a confident label
Builds on it 1 paper
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One of the aims of the present work is to extend these results by including the contributions of instantons that have not been included in the approximation used in [ref] .
Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds · The central charge and entropy · 1.00
Compares with it 1 paper
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The same result has been derived independently in [ref] in a much more elegant fashion, using group theoretic techniques.
Non-Supersymmetric Stringy Attractors · Introduction · 0.91
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