red string of fate
Refers to the East Asian folk belief that destined lovers are connected by an invisible red thread tied to their little fingers. Often used metaphorically for fated romantic connections.
See also: 赤い糸
When I met her, I felt this was the red string of fate.
It is said that two people connected by the red string of fate will eventually be united no matter what difficulties they face.
赤い糸 is a shorter form that can refer to the same concept but is less explicit about fate; 運命の赤い糸 explicitly includes the notion of destiny.
A phrase originating from Chinese folklore, later adopted into Japanese culture. The exact historical derivation is uncertain, but the concept of an invisible red thread connecting destined lovers is well-established in East Asian tradition.