Gauging the R-symmetry of old-minimal $R+R^2$ supergravity

Abstract

Old-minimal $R+R^2$ supergravity has a $U(1)$ R-symmetry which rotates the chiral curvature superfield. We gauge this R-symmetry and study new interactions involving the gauge multiplet in the context of inflation and supersymmetry breaking. We construct models where supersymmetry and the R-symmetry are spontaneously broken during and after Starobinsky inflation, and one-loop gauge anomalies are cancelled by the Green--Schwarz mechanism which can also generate Standard Model gaugino masses. The hierarchy between the auxiliary fields, $\langle F\rangle\gtrsim\langle D\rangle$, leads to split mass spectrum where the chiral multiplet masses are around the inflationary scale ($10^{13}$ GeV), while the gauge multiplet masses can be arbitrarily small.