Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Anti-Self-Dual Solutions

TL;DR

This paper classifies supersymmetric solutions in four-dimensional Euclidean supergravity with anti-self-dual Maxwell fields, linking them to solutions of the Toda equation and Einstein--Weyl structures, and characterizes Euclidean Kastor--Traschen metrics via special spinors.

Contribution

It provides a comprehensive classification of supersymmetric solutions with anti-self-dual Maxwell fields in minimal N=2 gauged Euclidean supergravity, connecting them to integrable systems and geometric structures.

Findings

Solutions are expressed via the SU(∞) Toda equation.

Anti-self-dual Einstein metrics are characterized by these solutions.

Euclidean Kastor--Traschen metrics are identified by specific super covariantly constant spinors.

Abstract

We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(\infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.