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

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.

Final version - to appear in CQG. Small changes in the manuscript and the title