Anti-self-dual Maxwell solutions on hyperk\"ahler manifold and N=2 supersymmetric Ashtekar gravity

TL;DR

This paper constructs anti-self-dual Maxwell solutions on hyperk"ahler manifolds and derives N=2 supersymmetric equations in Ashtekar gravity, revealing connections with supersymmetric Yang-Mills solutions and providing explicit examples.

Contribution

It introduces a novel link between ASD Maxwell solutions on hyperk"ahler manifolds and N=2 supersymmetric Ashtekar gravity equations, with explicit solution examples.

Findings

Constructed ASD Maxwell solutions on hyperk"ahler manifolds.

Derived N=2 supersymmetric half-flat equations in Ashtekar gravity.

Presented explicit examples of Maxwell solutions.

Abstract

Anti-self-dual (ASD) Maxwell solutions on 4-dimensional hyperk\"ahler manifolds are constructed. The N=2 supersymmetric half-flat equations are derived in the context of the Ashtekar formulation of N=2 supergravity. These equations show that the ASD Maxwell solutions have a direct connection with the solutions of the reduced N=2 supersymmetric ASD Yang-Mills equations with a special choice of gauge group. Two examples of the Maxwell solutions are presented.