Abstract
Using a reformulation of topological \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 2 QFT’s from all Gaiotto theories on arbitrary 4-manifolds.
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Cecotti, S., Gerig, C. & Vafa, C. G2 holonomy, Taubes’ construction of Seiberg-Witten invariants and superconducting vortices. J. High Energ. Phys. 2020, 38 (2020). https://doi.org/10.1007/JHEP04(2020)038
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DOI: https://doi.org/10.1007/JHEP04(2020)038