G(2) holonomy, Taubes' construction of Seiberg-Witten invariants and superconducting vortices

Using a reformulation of topological N = 2 QFT’s in M-theory setup, where QFT is realized via M5 branes wrapping co-associative cycles in a G2 manifold constructed from the space of self-dual 2-forms over a four-fold X, we show that superconducting vortices are mapped to M2 branes stretched between M5 branes. This setup provides a physical explanation of Taubes’ construction of the Seiberg-Witten invariants when X is symplectic and the superconducting vortices are realized as pseudo-holomorphic curves. This setup is general enough to realize topological QFT’s arising from N = 2 QFT’s from all Gaiotto theories on arbitrary 4-manifolds. © 2020, The Author(s).