Topics in Cubic Special Geometry

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.

1+39 pages

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Cited by in corpus (10)

• Symplectic Deformations of Gauged Maximal Supergravity
• The black-hole/qubit correspondence: an up-to-date review
• Special Vinberg Cones and the Entropy of BPS Extremal Black Holes
• Multiple Single-Centered Attractors
• Black hole solutions of N=2, d=4 supergravity with a quantum correction, in the H-FGK formalism
• ASK/PSK-correspondence and the r-map
• Peccei-Quinn Transformations and Black Holes : Orbit Transmutations and Entanglement Generation
• Non-Supersymmetric Stringy Attractors
• Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion