Quaternionic Extension of the Double Taub-NUT Metric

TL;DR

This paper constructs a new quaternion-K"ahler extension of the double Taub-NUT metric, providing a non-homogeneous Einstein metric with self-dual Weyl tensor, using harmonic superspace and quotient methods.

Contribution

It introduces a novel quaternion-K"ahler extension of the double Taub-NUT metric with specific isometry properties, expanding the class of known Einstein metrics.

Findings

Provides an explicit form of the quaternion-K"ahler extension

Demonstrates the metric has $U(1) imes U(1)$ isometry

Identifies the metric as non-homogeneous with self-dual Weyl tensor

Abstract

Starting from the generic harmonic superspace action of the quaternion-K\"ahler sigma models and using the quotient approach we present, in an explicit form, a quaternion-K\"ahler extension of the double Taub-NUT metric. It possesses $U(1)\times U(1)$ isometry and supplies a new example of non-homogeneous Einstein metric with self-dual Weyl tensor.