The cosmological constant in Supergravity

TL;DR

This paper introduces a new supersymmetric formulation of the cosmological constant in N=1 supergravity, using a novel gauge-invariant Fayet-Iliopoulos term that enables spontaneous supersymmetry breaking and vacuum energy uplifting.

Contribution

It proposes a new gauge-invariant FI term in supergravity that allows for a positive cosmological constant and spontaneous supersymmetry breaking, differing from previous formulations especially with matter present.

Findings

The new FI term is gauge invariant and compatible with Kähler transformations.

It can uplift the vacuum energy to a positive value, enabling de Sitter solutions.

The formulation reduces to a standard FI term in the absence of matter.

Abstract

We propose a supersymmetrisation of the cosmological constant in ordinary $N=1$ supergravity that breaks supersymmetry spontaneously by a constant Fayet-Iliopoulos (FI) term associated to a $U(1)$ symmetry. This term is a variation of a new gauge invariant FI term proposed recently, which is invariant under K\"{a}hler transformations and can be written even for a gauged R-symmetry on top of the standard FI contribution. The two terms are the same in the absence of matter but differ in its presence. The proposed term is reduced to a constant FI-term up to fermion interactions that disappear in the unitary gauge in the absence of any F-term supersymmetry breaking. The constant FI term leads to a positive cosmological constant, uplifting the vacuum energy from the usual anti-de Sitter supergravity to any higher value.