Euclidean N=2 Supergravity

TL;DR

This paper derives the Killing spinor equations for Euclidean N=2 supergravity coupled to vector multiplets, providing a foundation for discovering supersymmetric instanton solutions in Euclidean supersymmetric theories.

Contribution

It introduces the explicit form of Killing spinor equations in Euclidean N=2 supergravity with vector multiplets, extending the understanding of supersymmetric solutions in Euclidean settings.

Findings

Derived Killing spinor equations for Euclidean N=2 supergravity.

Established a basis for finding supersymmetric instanton solutions.

Connected Euclidean special geometry with supergravity solutions.

Abstract

Euclidean special geometry has recently been investigated in the context of Euclidean supersymmetric theories with vector multiplets. In the rigid case, the scalar manifold is described by affine special para-Kahler geometry while the target geometries of Euclidean vector multiplets coupled to supergravity are given by projective special para-Kahler manifolds. In this letter, we derive the Killing spinor equations of Euclidean N=2 supergravity theories coupled to vector multiplets. These equations provide the starting point for finding general supersymmetric instanton solutions.