Electric-magnetic duality in a class of G ₂-compactifications of M-theory

We study electric-magnetic duality in compactifications of M-theory on twisted connected sum (TCS) G₂ manifolds via duality with F-theory. Specifically, we study the physics of the D3-branes in F-theory compactified on a Calabi-Yau fourfold Y, dual to a compactification of M-theory on a TCS G₂ manifold X. N = 2 supersymmetry is restored in an appropriate geometric limit. In that limit, we demonstrate that the dual of D3-branes probing seven-branes corresponds to the shrinking of certain surfaces and curves, yielding light particles that may carry both electric and magnetic charges. We provide evidence that the Minahan-Nemeschansky theories with E_n flavor symmetry may be realized in this way. The SL(2, ℤ) monodromy of the 3/7-brane system is dual to a Fourier-Mukai transform of the dual IIA/M-theory geometry in this limit, and we extrapolate this monodromy action to the global compactification. Away from the limit, the theory is broken to N = 1 supersymmetry by a D-term.