Superconformal generalizations of auxiliary vector modified polynomial f(R) theories

We present the supersymmetric completion of the auxiliary vector modified polynomial $f(R)$ theories in their dual scalar-tensor theory formulation that interpolate between the auxiliary vector modified polynomial $f(R)$ theories and chaotic inflation with the power-law potential $V(\phi) \propto \phi^p$. The supersymmetrization is achieved in two steps: First, we introduce a superconformal theory for three chiral multiplets by choosing a conformal K\"ahler potential and a conformal superpotential. In the second step, we use one of the chiral multiplets to compensate for the superconformal symmetries and achieve the K\"ahler potential and the superpotential while the other two are used to realize inflation with a stable inflationary trajectory. The stability of the inflationary trajectory requires certain deformations to the K\"ahler potential which we discuss their compatibility against the inflationary observables from the latest Planck data.