Axisymmetric non-abelian BPS monopoles from G_2 metrics

TL;DR

This paper constructs exact self-gravitating BPS monopoles with $SU(2) imes U(1)$ symmetry from $G_2$ holonomy metrics, revealing novel topological charge configurations and connections to supersymmetric cosmic strings.

Contribution

It introduces a new class of exact monopole solutions derived from $G_2$ metrics, highlighting their axial symmetry and topological properties, and links to supersymmetric cosmic strings.

Findings

Solutions carry two topological charges.

Solutions are generally axially symmetric, not spherically symmetric.

Some $G_2$ metrics reduce to supersymmetric cosmic strings.

Abstract

Exact $SU(2)\times U(1)$ self-gravitating BPS global monopoles in four dimensions are constructed by dimensional reduction of eight dimensional metrics with $G_2$ holonomy asymptotic to cones over $S^3\times S^3$. The solutions carry two topological charges in an interesting way. They are generically axially but not spherically symmetric. This last fact is related to the isometries and asymptotic topology of the $G_2$ metrics. It is further shown that some $G_2$ metrics known numerically reduce to supersymmetric cosmic strings.