De Sitter solutions in N=4 matter coupled supergravity

TL;DR

The paper analyzes gauged N=4 supergravity in four dimensions with matter and a positive cosmological constant, focusing on the interplay between the SU(1,1)/U(1) scalars and matter scalars. It derives the full scalar potential, identifies extremum conditions for the SU(1,1)/U(1) sector, and provides an explicit parametrization of the matter-sector constraints using an SO(6,6+n) framework, specializing to six vector multiplets. Through three explicit gauge-group examples (SO(3)^4, SO(3)^2 × SO(2,1)^2, and SO(2,1)^4), it demonstrates scenarios with positive extrema, including a genuine absolute minimum in noncompact gaugings, while highlighting potential issues with kinetic-term signs and the relation between V0 and second derivatives. The work expands the landscape of de Sitter vacua in extended supergravity and lays groundwork for future cosmological applications and stability analyses.

Abstract

We investigate the scalar potential of gauged N=4 supergravity with matter. The extremum in the SU(1,1)/U(1) scalars is obtained for an arbitrary number of matter multiplets. The constraints on the matter scalars are solved in terms of an explicit parametrisation of an SO(6,6+n) element. For the case of six matter multiplets we discuss both compact and noncompact gauge groups. In an example involving noncompact groups and four scalars we find a potential with an absolute minimum and a positive cosmological constant.