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 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.
Highlights
It is well known that the cosmological constant in supergravity is highly constrained
We propose a supersymmetrisation of the cosmological constant in ordinary N = 1 supergravity that breaks supersymmetry spontaneously by a constant FayetIliopoulos (FI) term associated to a U (1) symmetry
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
Summary
It is well known that the cosmological constant in supergravity is highly constrained. We propose a modification/generalisation of this FI term that has the following properties: (1) it can be written independently whether the corresponding U (1) gauges or not the R-symmetry; (2) in the absence of matter fields and in the case of an ordinary (non-R) U (1), it coincides with the one proposed in [8]; (3) in the case of a U (1)R, it can be written on top of the standard constant FI term; (4) in the presence of matter fields the action is invariant under Kähler transformations and its bosonic contribution is always a constant FI term that uplifts in particular the vacuum energy by an arbitrary positive constant. We have two appendices; “Appendix A” contains useful formulae used in the text, while in “Appendix B” we compute the fermionic part of the supergravity action
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