Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality

TL;DR

This paper constructs new supersymmetric solutions in Euclidean Einstein-Maxwell theory with a cosmological constant, expanding beyond self-dual fields, and classifies them into three distinct solution types based on their properties.

Contribution

It introduces three novel classes of supersymmetric solutions with non-self-dual Maxwell fields in Euclidean Einstein-Maxwell theory, including a Euclidean Kastor-Traschen solution.

Findings

Identified three classes of solutions depending on field and cosmological constant signs.

Connected solutions to known Lorentzian supersymmetric solutions.

Constructed solutions involving hyper-CR Einstein-Weyl structures.

Abstract

We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in arXiv:0804.0009, hep-th/0406238 . The second class is constructed from a three dimensional base space which admits a hyper-CR Einstein-Weyl structure. The third class is the Euclidean Kastor-Traschen solution.