Abstract
We study non-supersymmetric extremal black hole excitations of 4d mathcal{N} = 2 supersymmetric string vacua arising from compactification on Calabi-Yau threefolds. The values of the (vector multiplet) moduli at the black hole horizon are governed by the attractor mechanism. This raises natural questions, such as “what is the distribution of attractor points on moduli space?” and “how many attractor black holes are there with horizon area up to a certain size?” We employ tools developed by Denef and Douglas [1] to answer these questions.
Highlights
JHEP10(2020)042 fantastic success of string theory in counting microstates of BPS black holes [13] to the extremal but non-BPS case
First questions one might ask are ‘How are attractor moduli distributed in moduli space?’ and ‘How many attractors exist with entropy below some cutoff S∗?’ Denef and Douglas [1] attacked these problems in the BPS case, using tools that they had developed for studying flux compactifications
We have studied the distribution of the attractor moduli of nonsupersymmetric extremal black holes in the complex structure moduli space of Calabi-Yau threefolds
Summary
Consider a 4d gravity theory with U(1) gauge fields and moduli φi coupled to the gauge fields via axio-dilaton-like couplings:. The authors of [7] studied ansatze parametrized by choices of electric and magnetic charges that determine extremal black holes in such a theory. They found that solutions are associated to local minima of an effective potential, Veff (φi). Potential to be independent of some moduli In this case, these moduli will not be attracted, and the entropy of an extremal black hole will not depend on them. CI ∧ γ = QJ CI ∧ CJ = ΣIJ QJ ≡ QI Another important function of this basis is to provide convenient coordinates on M, namely the periods of Ω: ΠI = CI ∧ Ω.
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