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Register a new userExtremal Black Hole and Flux Vacua Attractors
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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 $3leqslant Nleqslant 8$, d=4 supergravities are reported.
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We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space.
We present the simplest model for classical transitions in flux vacua. A complex field with a spontaneously broken U(1) symmetry is embedded in $M_2times S_1$. We numerically construct different winding number vacua, the vortices interpolating between them, and simulate the collisions of these vortices. We show that classical transitions are generic at large boosts, independent of whether or not vortices miss each other in the compact $S_1$.
We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa-Witten superpotential is exponentially small. We present an example with $W_0 approx 2 times 10^{-8}$ on an orientifold of a Calabi-Yau hypersurface with $(h^{1,1},h^{2,1})=(2,272)$, at large complex structure and weak string coupling.
We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously.
Based on the numerical conformal bootstrap bound, we show that the arbitrarily small Reissner-Nordstrom black hole in AdS space-time is inconsistent with holography unless the energy spectrum is modified quantum mechanically or it is unstable as indicated by the weak gravity conjecture.
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