Gauged R-symmetry and its anomalies in 4D N=1 supergravity and phenomenological implications

Understand

We consider a class of models with gauged U(1)_R symmetry in 4D N=1 supergravity that have, at the classical level, a metastable ground state, an infinitesimally small (tunable) positive cosmological constant and a TeV gravitino mass.

• We analyse if these properties are maintained under the addition of visible sector (MSSM-like) and hidden sector state(s), where the latter may be needed for quantum consistency.
• We then discuss the anomaly cancellation conditions in supergravity as derived by Freedman, Elvang and K\"ors and apply their results to the special case of a U(1)_R symmetry, in the presence of the Fayet-Iliopoulos term ($\xi$) and Green-Schwarz mechanism(s).
• We investigate the relation of these anomaly cancellation conditions to the "naive" field theory approach in global SUSY, in which case U(1)_R cannot even be gauged.