Distributions of extremal black holes in Calabi-Yau compactifications
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Springer
Received: December 10, Revised: August 30, Accepted: September 11, Published: October 7,
2019 2020 2020 2020
George Hulsey, Shamit Kachru, Sungyeon Yang and Max Zimet Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305 U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We study non-supersymmetric extremal black hole excitations of 4d 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. Keywords: Black Holes in String Theory, Supergravity Models ArXiv ePrint: 1901.10614
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)042
JHEP10(2020)042
Distributions of extremal black holes in Calabi-Yau compactifications
Contents 1
2 The attractor mechanism in type IIB Calabi-Yau compactifications
2
3 Distributions of attractors 3.1 DF ≈ 0 3.2 Conifold
5 8 9
4 Numerical verification
10
5 Conclusion
13
1
Introduction
The attractor mechanism [2–4] is a ubiquitous phenomenon in gravitational theories with moduli whereby the moduli take on values at the horizon of an extremal1 (zero temperature) black hole that are independent2 of their values at infinity. It can be heuristically motivated (see, e.g., [7]) by noting that the entropy of such a black hole — being the logarithm of an integer — should vary discretely, while the moduli vary continuously. Alternatively, it can be understood geometrically from the fact that extremal black holes have an infinite throat so that the physical distance to the horizon is infinite, and variations of the moduli over this distance wash away any dependence on the moduli at infinity [8]. Ultimately it follows from an analysis of the solutions of the equations of motion [2–4, 7–10]. The discussion thus far has made no reference to supersymmetry, but of course the latter is intimately connected to the attractor mechanism. One reason is that the very existence of moduli is generically unnatural without supersymmetry. Another is that the study of BPS attractors is greatly simplified by the first-order Killing spinor equation. However, one can study non-supersymmetric but extremal black holes arising as excitations of supersymmetric vacuum solutions. This makes it natural to study extremal but non-BPS attractors in supergravity. A particularly natural setting for such a study is in the context of string theory [11]. One important reason is that the attractor mechanism implies a sort of non-renormalization theorem which, under certain conditions, allows one to compute the entropy of a weaklycoupled collection of microscopic ingredients
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