We study the embedding of the quadratic model of chaotic inflation into the 4D, N=1 minimal theories of supergravity by the use of massive vector multiplets and investigate its robustness against higher order corrections. In particular, we investigat
e the criterion of technical naturalness for the inflaton potential. In the framework of the new-minimal formulation the massive vector multiplet is built in terms of a real linear multiplet coupled to a vector multiplet via the 4D analog of the Green-Schwarz term. This theory gives rise to a single-field quadratic model of chaotic inflation, which is protected by an shift symmetry which naturally suppresses the higher order corrections. The embedding in the old-minimal formulation is again achieved in terms of a massive vector multiplet and also gives rise to single-field inflation. Nevertheless in this case there is no obvious symmetry to protect the model from higher order corrections.
We calculate the low energy effective action of massless and massive complex linear superfields coupled to a massive U(1) vector multiplet. Our calculations include superspace higher derivative corrections and therefore go beyond previous results. Am
ong the superspace higher derivatives we find that terms which lead to a deformation of the auxiliary field potential and may break supersymmetry are also generated. We show that the supersymmetry breaking vacua can only be trusted if there exists a hierarchy between the higher order terms. A renormalization group analysis shows that generically a hierarchy is not generated by the quantum corrections.
In the N=1 four-dimensional new-minimal supergravity framework, we supersymmetrise the coupling of the scalar kinetic term to the Einstein tensor. This coupling, although introduces a non-minimal derivative interaction of curvature to matter, it does
not introduce harmful higher-derivatives. For this construction, we employ off-shell chiral and real linear multiplets. Physical scalars are accommodated in the chiral multiplet whereas curvature resides in a linear one.
We consider compactifications induced by the gravitino field of eleven dimensional supergravity. Such compactifications are not trivial in the sense that the gravitino profiles are not related to pure bosonic ones by means of a supersymmetry transfor
mation. The basic property of such backgrounds is that they admit $psi$-torsion although they have vanishing Riemann tensor. Thus, these backgrounds may be considered also as solutions of the teleparallel formulation of supergravity. We construct two classes of solutions, one with both antisymmetric three-form field, gravity and gravitino and one with only gravity and gravitino. In these classes of solutions, the internal space is a parallelized compact manifold, so that it does not inherit any cosmological constant to the external spacetime. The latter turns out to be flat Minkowski in the maximally symmetric case. The elimination of the cosmological constant in the spontaneously compactified supergravity seems to be a generic property based on the trading of the cosmological constant for parallelizing torsion.
