N=2 supergravity models with stable de Sitter vacua

TL;DR

The paper addresses the problem of obtaining stable de Sitter vacua within $N=2$ supergravity, a long-standing challenge in extended supergravities. It advances a method based on gauging non-compact isometries with Fayet-Iliopoulos terms and a controlled symplectic rotation of the embedding to generate a positive scalar potential. The main results are explicit constructions with $n=3$ and $n=5$ vector multiplets (with and without hypermultiplets) that yield a plane of stable de Sitter points, where certain scalar directions are eaten by gauge fields and the remaining spectrum has positive de Sitter Casimir eigenvalues $k=3,6$, signaling stability in the classical theory. In addition, a model with hypermultiplets shows similar vacua but introduces quaternionic zero modes, highlighting the need for quantum corrections to assess full stability. These findings provide rare, explicit examples of stable de Sitter backgrounds in extended supergravity with potential cosmological relevance and guide future exploration toward maximal theories and quantum effects.

Abstract

In the present talk I shall review the construction of N=2 supergravity models exhibiting stable de Sitter vacua. These solutions represent the first instance of stable backgrounds with positive cosmological constant in the framework of extended supergravities (N >=2). After briefly reviewing the role of de Sitter space--times in inflationary cosmology, I shall describe the main ingredients which were necessary for the construction of gauged N=2 supergravity models admitting stable solutions of this kind.

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