Attractors in Supergravity

Abstract

The concept of attractors, well-known in classical mechanics, proved to be very productive in supergravity, in the theory of black holes and inflationary cosmology. We start with attractors in supersymmetric black holes and discuss also non-BPS black hole attractors. Recently the non-BPS case helped to explain, via enhanced dualitiy symmetry, mysterious cancellation of ultraviolet divergences in 82 Feynman diagrams in 4-loop superamplitude in $N=5$ supergravity. We discuss the implications of these results for the possibility of the all-loop finiteness of $N > 4$ 4D supergravities. We continue with the description of inflationary $\alpha$-attractors. This large class of inflationary models gives predictions that are stable with respect to even very significant modifications of inflationary potentials. These predictions match all presently available CMB-related cosmological data. These models provide targets for the future satellite mission LiteBIRD, which will attempt to detect primordial gravitational waves. We describe some of the recent advanced versions of cosmological attractors which have a beautiful fractal landscape structure. Invited contribution to "Half a century of Supergravity", eds.~A. Ceresole and G.~Dall'Agata (Cambridge Univ. Press, to appear)