G 2 holonomy, Taubes’ construction of Seiberg-Witten invariants and superconducting vortices

• Main Authors: Sergio Cecotti, Chris Gerig, Cumrun Vafa
• Format: Article
• Language: English
• Published: SpringerOpen 2020-04-01
• Series: Journal of High Energy Physics
• Subjects: Differential and Algebraic Geometry; Supersymmetry and Duality; Topological Field Theories
• Online Access: http://link.springer.com/article/10.1007/JHEP04(2020)038

Abstract Using a reformulation of topological N $$ \mathcal{N} $$ = 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 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 $$ \mathcal{N} $$ = 2 QFT’s from all Gaiotto theories on arbitrary 4-manifolds.