Consequences of Supergravity with Gauged $\rm U(1)_R$ Symmetry

TL;DR

This work investigates the consequences of gauging the $U(1)_R$ symmetry within ${\cal N}=1$ supergravity, showing that a careful hidden-sector construction can yield $V_{\min}=0$ and $\langle D\rangle=0$, thereby breaking SUSY and $R$-symmetry at the Planck scale while decoupling the heavy $R$-vector multiplet from low-energy physics. A key result is that, despite the gauging, all direct low-energy effects of the $U(1)_R$ gauge coupling vanish due to cancellations in the D-terms and the heavy-field integration, leaving a conventional MSSM-like theory with soft SUSY breaking and a small set of light remnants to address anomaly cancellation and hidden-sector dynamics. An explicit, anomaly-free complete model is presented, incorporating additional SM-charged fields and hidden-sector multiplets, and it employs non-minimal gauge kinetic terms to generate gluino masses. The paper further discusses the low-energy potential, possible axion-like states from broken global symmetries, and the phenomenological implications, including proton stability and challenges for grand unification. Overall, gauged $U(1)_R$ can be a hidden feature of SUSY breaking that leaves a familiar low-energy landscape but with distinctive remnants and consistency conditions requiring extra states beyond the MSSM.

Abstract

The structure of gauged R supergravity Lagrangians is reviewed, and we consider models with a hidden sector plus light fields of the MSSM. A simple potential for the hidden sector is presented which has a global minimum with zero cosmological constant and spontaneously broken SUSY and R-symmetry. The $\rm U(1)_R$ vector multiplet acquires a Planck scale mass through the Higgs mechanism, and it decouples at low energy. Due to very interesting cancellations, the $\rm U(1)_R$ D-terms also drop out at low energy. Thus no direct effects of the gauging of R-symmetry remain in the low energy effective Lagrangian, and this result is model independent, requiring only that R-symmetry be broken at the Planck scale and $<D> = 0$, where $D$ is the auxiliary field of the $\rm U(1)_R$ vector multiplet. The low energy theory is fairly conventional with soft SUSY breaking terms for the MSSM fields. As a remnant of the gauging of R-symmetry, it also contains light fields, some required to cancel R-anomalies and others from the hidden sector.