  We study electric-magnetic duality in compactifications of M-theory on
twisted connected sum (TCS) $G_2$ 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
$G_2$ manifold $X$. $\mathcal{N}=2$ 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 $SL(2,\mathbb{Z})$ 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
$\mathcal{N}=1$ supersymmetry by a D-term.
