Axisymmetric non-abelian BPS monopoles from G_2 metrics

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.