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

TL;DR

This paper explores gauged U(1)_R symmetry in 4D N=1 supergravity, analyzing anomaly cancellation, stability, and phenomenological implications, especially regarding a tunable TeV-scale gravitino mass and the constraints on U(1)_R charges.

Contribution

It provides a detailed analysis of anomaly cancellation conditions in supergravity with gauged U(1)_R symmetry and their impact on phenomenological models with a small positive cosmological constant.

Findings

Anomaly cancellation conditions are similar in supergravity and global SUSY approaches.

A stable, metastable ground state with a TeV-scale gravitino mass is possible under certain charge constraints.

Constraints on U(1)_R charges influence the stability and phenomenology of the models.

Abstract

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. We show the two approaches give similar conditions. Their induced constraints at the phenomenological level, on the above models, remain strong even if one lifted the GUT-like conditions for the MSSM gauge couplings. In an anomaly-free model, a tunable, TeV-scale gravitino mass may remain possible provided that the U(1)_R charges of additional hidden sector fermions (constrained by the cubic anomaly alone) do not conflict with the related values of U(1)_R charges of their scalar superpartners, constrained by existence of a stable ground state. This issue may be bypassed by tuning instead the coefficients of the Kahler connection anomalies (b_K, b_{CK}).