St\"uckelberg path to pure de Sitter supergravity

TL;DR

This paper develops a finite formulation of unimodular supergravity using the super-St"uckelberg mechanism, enabling all-order construction of de Sitter solutions in ${ m N}=1$ supergravity, bridging perturbative and complete theories.

Contribution

It introduces a recursive, all-order super-St"uckelberg approach for pure de Sitter supergravity, extending previous perturbative methods to a complete finite formulation.

Findings

Constructed a complete four-dimensional action with de Sitter solutions.

Extended super-St"uckelberg transformations beyond second order.

Bridged perturbative approaches with a finite supergravity theory.

Abstract

We advance the study of pure de Sitter supergravity by introducing a finite formulation of unimodular supergravity via the super-St\"uckelberg mechanism. Building on previous works, we construct a complete four-dimensional action of spontaneously broken ${\cal N}\!\!=\!\!1$ supergravity to all orders, which allows for de Sitter solutions. The introduction of finite supergravity transformations extends the super-St\"uckelberg procedure beyond the second order, offering a recursive solution to all orders in the goldstino sector. This work bridges the earlier perturbative approaches and the complete finite theory, opening new possibilities for de Sitter vacua in supergravity models and eventually string theory.