Nekrasov Functions and the $SU(2)$ Calogero–Moser System

The prepotential in supersymmetric field theories is an analog of the Lagrangian function in classical mechanics. N. Nekrasov suggested a generalization of the prepotential by introducing a pair of additional parameters $\{\epsilon_1, \epsilon_2\}$. In this paper, we construct the one-parametric Nekrasov prepotential depending on $\{\epsilon_1, \epsilon_2\}=\{\epsilon_1, 0\}$ by using the monodromies of the corresponding Calogero–Moser system. This correspondence establishes a natural relationship between supersymmetric field theories and integrable Hamiltonian systems.