Extremal Black Hole and Flux Vacua Attractors

TL;DR

This paper reviews the Attractor Mechanism in four-dimensional supergravity frameworks, explaining how it stabilizes moduli and scalars in extremal black holes and flux compactifications, with detailed analyses and recent advances.

Contribution

It provides a comprehensive pedagogical comparison of the Attractor Mechanism in black hole and flux compactification contexts, including new insights into U-duality orbits and non-BPS attractors.

Findings

Analysis of criticality conditions and New Attractor approaches

Stringy Hodge-decomposition techniques applied to compactifications

Recent results on U-duality orbits of non-BPS black hole attractors

Abstract

These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\frac{CY_{3}\times T^{2}}{\mathbb{Z}_{2}}$. Finally, recent results on the U-duality orbits and moduli spaces of non-BPS extremal black hole attractors in $3\leqslant N\leqslant 8$, d=4 supergravities are reported.