Supersymmetric Gauge Theories and Gravitational Instantons

TL;DR

This paper explores the connection between three-dimensional gauge theories, gravitational instantons, and monopoles, modeling self-dual gravitational instantons of D_k-type as moduli spaces of singular monopoles and analyzing their twistor spaces and metrics.

Contribution

It introduces a novel approach to model D_k-type gravitational instantons as moduli spaces of singular monopoles, providing explicit constructions of their twistor spaces and metrics.

Findings

Modeling of D_k gravitational instantons as monopole moduli spaces

Explicit construction of twistor spaces for these instantons

Derivation of their metrics and geometric properties

Abstract

Various string theory realizations of three-dimensional gauge theories relate them to gravitational instantons, Nahm equations and monopoles. We use this correspondence to model self-dual gravitational instantons of $D_k$-type as moduli spaces of singular monopoles, find their twistor spaces and metrics.