Phenomenological aspects of supergravity theories in de Sitter vacua

Abstract

We introduce an $N=1$ supergravity model based on the gauged shift symmetry of a single chiral multiplet, which can be identified with the string dilaton or a compactification modulus. The model allows for a tunably small and positive value of the cosmological constant. The gravitino mass parameter and the dilaton Vacuum Expectation Value are separately tunable. In a second part we analyze the quantum consistency of these models. Recent work on anomalies in supergravity theories with Fayet-Iliopoulos terms was extended, such that their results can be interpreted from a field-theoretic point of view. We show that for certain values of the parameters the anomaly cancellation conditions are inconsistent with a TeV gravitino mass. In the third part the above model is used as a hidden sector for supersymmetry breaking. In its minimal version, the model leads to tachyonic scalar soft masses. This problem can however be circumvented by the introduction of an extra Pol\'onyi-like hidden sector field, or by allowing for non-canonical kinetic terms for the Standard Model fields, while maintaining the desirable features of the model. The resulting low energy spectrum consists of very light neutralinos, charginos and gluinos, while the squarks remain heavy, with the exception of the stop squark which can be as light as 2 TeV. Finally, we discus possibility that the shift symmetry is identified with known global symmetries of the MSSM. The particular cases where this global symmetry is Baryon minus Lepton number ($B-L$), or $3B-L$, which contain the known R-parity or matter parity of the MSSM, are analyzed in great detail. It is shown that the phenomenology is similar to the above case where the MSSM fields are inert, with the exception of the stop squark, which can be as light as $1.5$ TeV.