# Simple Sinflaton-less $\alpha$-attractors

## TL;DR

This paper develops the simplest supergravity models of $ ext{alpha}$-attractors with only the inflaton as the scalar degree of freedom, eliminating additional scalars like sinflaton and sgoldstino.

## Contribution

It introduces a minimal supergravity construction of $ ext{alpha}$-attractors with a single scalar, using orthogonal nilpotent superfields to remove extra scalars from the spectrum.

## Key findings

- Models contain only the inflaton, graviton, and massive gravitino.
- The orthogonality condition simplifies the Kähler potential.
- Framework aligns with $ ext{D3}$-induced geometric inflation.

## Abstract

We construct the simplest inflationary $\alpha$-attractor models in supergravity: it has only one scalar, the inflaton. There is no sinflaton since the inflaton belongs to an orthogonal nilpotent superfield where the sinflaton depends on fermion bilinears. When the local supersymmetry is gauge-fixed, these models have only one single real scalar (the inflaton), a graviton and a massive gravitino. The sinflaton, sgoldstino and inflatino are all absent from the physical spectrum in the unitary gauge. The orthogonality condition leads to the simplest K\"ahler potential for the inflaton, while preserving the Poincar\'e disk geometry of $\alpha$-attractors. The models are particularly simple in the framework of the $\overline {D3}$ induced geometric inflation.