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Using a reformulation of topological ${\cal N}=2$ QFT's in M-theory setup,where QFT is realized via M5 branes wrapping co-associative cycles in a $G_2$manifold constructed from the space of self-dual 2-forms over $X^4$, we showthat superconducting vortices are mapped to M2 branes stretched between M5branes. This setup provides a physical explanation of Taubes' construction ofthe Seiberg-Witten invariants when $X^4$ is symplectic and the superconductingvortices are realized as pseudo-holomorphic curves. This setup is generalenough to realize topological QFT's arising from ${\cal N}=2$ QFT's from allGaiotto theories on arbitrary 4-manifolds.

$G_2$ Holonomy, Taubes' Construction of Seiberg-Witten Invariants and Superconducting Vortices