Minimal R+R2 supergravity models of inflation coupled to matter

The supersymmetric extension of “Starobinsky” R+αR2 models of inflation is particularly simple in the “new minimal” formalism of supergravity, where the inflaton has no scalar superpartners. This paper is devoted to matter couplings in such supergravity models. We show how in the new minimal formalism matter coupling presents certain features absent in other formalisms. In particular, for the large class of matter couplings considered in this paper, matter must possess an R-symmetry, which is gauged by the vector field which becomes dynamical in the “new minimal” completion of the R+αR2 theory. Thus, in the dual formulation of the theory, where the gauge vector is part of a massive vector multiplet, the inflaton is the superpartner of the massive vector of a nonlinearly realized R-symmetry. The F-term potential of this theory is of no-scale type, while the inflaton potential is given by the D-term of the gauged R-symmetry. The absolute minimum of the potential is always exactly supersymmetric, so in this class of models if realistic vacua exist, they must be always metastable. We also briefly comment on possible generalizations of the examples discussed here and we exhibit some features of higher-curvature supergravity coupled to matter in the “old minimal” formalism

Supersymmetry breaking by higher dimension operators

We discuss a supersymmetry breaking mechanism for <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> theories triggered by higher dimensional operators. We consider such operators for real linear and chiral spinor superfields that break supersymmetry and reduce to the Volkov–Akulov action. We also consider supersymmetry breaking induced by a higher dimensional operator of a nonminimal scalar (complex linear) multiplet. The latter differs from the standard chiral multiplet in its auxiliary sector, which contains, in addition to the complex scalar auxiliary of a chiral superfield, a complex vector and two spinors auxiliaries. By adding an appropriate higher dimension operator, the scalar auxiliary may acquire a nonzero vev triggering spontaneous supersymmetry breaking. We find that the spectrum of the theory in the supersymmetry breaking vacuum consists of a free chiral multiplet and a constraint chiral superfield describing the goldstino. Interestingly, the latter turns out to be one of the auxiliary fermions, which becomes dynamical in the supersymmetry breaking vacuum. In all cases we are considering here, there is no sgoldstino mode and thus the goldstino does not have a superpartner. The sgoldstino is decoupled since the goldstino is one of the auxiliaries, which is propagating only in the supersymmetry breaking vacuum. We also point out how higher dimension operators introduce a potential for the propagating scalar of the theory