Eur. Phys. J. C (2018) 78: 718
https://doi.org/10.1140/epjc/s10052-018-6175-4

Regular Article - Theoretical Physics

The cosmological constant in supergravity

¹ Laboratoire de Physique Théorique et Hautes Énergies, LPTHE, Sorbonne Université, CNRS, 4 Place Jussieu, 75005, Paris, France
² Albert Einstein Center, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
³ Department of Physics, Faculty of Science, Chulalongkorn University, Phayathai Road, Pathumwan, Bangkok, 10330, Thailand

^* e-mail: dma3ac2@gmail.com

Received: 16 May 2018
Accepted: 22 August 2018
Published online: 5 September 2018

Abstract

We propose a supersymmetrisation of the cosmological constant in ordinary 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 Kähler 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.