Abstract:We construct the component action of the system including an ordinary matter and a nilpotent multiplet in global and local supersymmetric framework. The higher dimensional operators of not only Goldstino but also matter and gravitino fields are shown, which appear due to nonlinearly realized supersymmetry.

Extending the work of Ferrara and one of the authors [1], we present dynamical cosmological models of α-attractors with plateau potentials for 3α = 1, 2, 3, 4, 5, 6, 7. These models are motivated by geometric properties of maximally supersymmetric theories: Mtheory, superstring theory, and maximal N = 8 supergravity. After a consistent truncation of maximal to minimal supersymmetry in a seven-disk geometry, we perform a two-step procedure: 1) we introduce a superpotential, which stabilizes the moduli of the seven-disk geometry in a supersymmetric minimum, 2) we add a cosmological sector with a nilpotent stabilizer, which breaks supersymmetry spontaneously and leads to a desirable class of cosmological attractor models. These models with n s consistent with observational data, and with tensor-to-scalar ratio r ≈ 10 −2 − 10 −3 , provide natural targets for future B-mode searches. We relate the issue of stability of inflationary trajectories in these models to tessellations of a hyperbolic geometry.

Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and gravitino mass. We illustrate it by providing generalized versions of polynomial chaotic inflation, Tand E-models of α-attractor type, disk merger. We also describe a multi-stage cosmological attractor regime, which we call cascade inflation.

We construct a model of natural inflation in the context of α-attractor supergravity, in which both the dilaton field and the axion field are light during inflation, and the inflaton may be a combination of the two. The T-model version of this theory is defined on the Poincaré disk with radius |Z| = 1. It describes a Mexican hat potential with the flat axion direction corresponding to a circle of radius |Z| < 1. The axion decay constant f a in this theory can be exponentially large because of the hyperbolic geometry of the Poincaré disk. Depending on initial conditions, this model may describe α-attractor inflation driven by the radial component of the inflaton field, natural inflation driven by the axion field, or a sequence of these two regimes. We also construct the E-model version of this theory, which have similar properties. In addition, we describe generalized α-attractor models where the potential can be singular at the boundary of the moduli space, and show that they can provide a simple solution for the problem of initial conditions for the models with plateau potentials.

An anti-D3-brane plays a crucial role in the construction of semirealistic cosmological models in string theory. Part of its action provides an uplift term that has been used to lift anti-de Sitter solutions to phenomenologically viable de Sitter vacua in the Kachru-Kallosh-Linde-Trivedi and large volume scenario (LVS) setups. In the last few years it has been shown that this uplift breaks supersymmetry spontaneously and can be described in the four-dimensional N ¼ 1 supergravity language by using constrained supermultiplets. Here we derive the complete four-dimensional N ¼ 1 supergravity action for an anti-D3-brane coupled to all closed-string background fields. In particular, we include the vector field, the scalar fields, and all fermions that live on the anti-D3-brane.