# Euclidean Supergravity

## TL;DR

This paper constructs a comprehensive four-dimensional Euclidean supergravity theory with eight supercharges, detailing its off-shell formulation, multiplet calculus, and differences from Minkowski space, including unbounded actions.

## Contribution

It provides the first full non-linear off-shell Euclidean supergravity formulation with a complete multiplet calculus, extending Minkowski results to Euclidean space.

## Key findings

- Off-shell Euclidean supergravity constructed with full multiplet calculus
- Hypermultiplets included with on-shell supersymmetry
- Euclidean actions are generally unbounded from below

## Abstract

Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincar\'e supergravity by introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.