  In this work we establish that the Inozemtsev system is the Seiberg-Witten
integrable system encoding the Coulomb branch physics of 4d $\mathcal{N}=2$
USp(2N) gauge theory with four fundamental and (for $N \geq 2$) one
antisymmetric tensor hypermultiplets. We describe the transformation from the
spectral curves and canonical one-form of the Inozemtsev system in the $N=1$
and $N=2$ cases to the Seiberg-Witten curves and differentials explicitly,
along with the explicit matching of the modulus of the elliptic curve of
spectral parameters to the gauge coupling of the field theory, and of the
couplings of the Inozemtsev system to the field theory mass parameters. This
result is a particular instance of a more general correspondence between
crystallographic elliptic Calogero-Moser systems with Seiberg-Witten integrable
systems, which will be explored in future work.
