Metastable de Sitter vacua in N=2 to N=1 truncated supergravity

TL;DR

This paper investigates the conditions under which metastable de Sitter vacua can exist in truncated supergravity theories, highlighting geometric constraints and the importance of projecting out tachyons to achieve metastability.

Contribution

It provides a detailed analysis of metastability conditions in N=2 to N=1 truncated supergravities, especially focusing on quaternionic manifolds and the universal hypermultiplet.

Findings

De Sitter vacua are necessarily unstable in N=2 theories with quaternionic manifolds.

Metastable de Sitter vacua are possible in N=1 theories with suitable superpotentials.

In weakly coupled regimes, de Sitter vacua are unstable; they may be metastable in strongly coupled regimes.

Abstract

We study the possibility of achieving metastable de Sitter vacua in general N=2 to N=1 truncated supergravities without vector multiplets, and compare with the situations arising in N=2 theories with only hypermultiplets and N=1 theories with only chiral multiplets. In N=2 theories based on a quaternionic manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable, as a result of the peculiar properties of the geometry. In N=1 theories based on a Kahler manifold and a superpotential, de Sitter vacua can instead be metastable provided the geometry satisfies some constraint and the superpotential can be freely adjusted. In N=2 to N=1 truncations, the crucial requirement is then that the tachyon of the mother theory be projected out from the daughter theory, so that the original unstable vacuum is projected to a metastable vacuum. We study the circumstances under which this may happen and derive general constraints for metastability on the geometry and the gauging. We then study in full detail the simplest case of quaternionic manifolds of dimension four with at least one isometry, for which there exists a general parametrization, and study two types of truncations defining Kahler submanifolds of dimension two. As an application, we finally discuss the case of the universal hypermultiplet of N=2 superstrings and its truncations to the dilaton chiral multiplet of N=1 superstrings. We argue that de Sitter vacua in such theories are necessarily unstable in weakly coupled situations, while they can in principle be metastable in strongly coupled regimes.