The c-map, Tits Satake subalgebras and the search for N = 2 inflaton potentials

In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) N = 2 supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the N = 2 supergravities we are able to make a general statement on the possible α-attractor models which can obtained upon truncation. We find that in symmetric N = 2 models group theoretical constraints restrict the allowed values of the parameter α to be α = 1, (2)/(3), (1)/(3). This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric N = 2 supergravities, in particular on the so called c-map connection between Quaternionic Kaehler manifolds starting from Special Kaehler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically selfcontained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of N = 2 supergravities is reviewed in some detail. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)