Vacuum structure in a chiral R+R^n modification of pure supergravity

Understand

We discuss an ${\cal R}+{\cal R}^n$ class of modified ${\cal N}=1$, D=4 supergravity models where the deformation is a monomial ${\cal R}^n\big|_F$ in the chiral scalar curvature multiplet ${\cal R}$ of the "old minimal" auxiliary field formulation.

• The scalaron and goldstino multiplets are dual to each other in this theory.
• Since one of them is not dynamical, this theory, as recently shown, cannot be used as the supersymmetric completion of $R+R^n$ gravity.
• This is confirmed by investigating the scalar potential and its critical points in the dual standard supergravity formulation with a single chiral multiplet with specific K\"ahler potential and superpotential.