On Quantum Special Kaehler Geometry

Abstract

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry.

1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 29

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• Black hole solutions of N=2, d=4 supergravity with a quantum correction, in the H-FGK formalism
• Black Holes and Groups of Type E7
• Magic Coset Decompositions
• Non-perturbative black holes in Type-IIA String Theory vs. the No-Hair conjecture
• Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• Regular 3-charge 4D black holes and their microscopic description