New $G_2$-conifolds in $M$-theory and their Field Theory Interpretation

A recent theorem of Foscolo-Haskins-Nordstr"om which constructs complete $G_2$-holonomy orbifolds from circle bundles over Calabi-Yau cones can be utilised to construct and investigate a large class of generalisations of the $M$-theory flop transition. We see that in many cases a UV perturbative gauge theory appears to have an infrared dual described by a smooth $G_2$-holonomy background in $M$-theory. Various physical checks of this proposal are carried out affirmatively.