Angular momentum and gravimagnetization of the $\mathcal{N}{=}2$ supersymmetric vacuum

We consider the gravimagnetization of the $\mathcal N=2$ supersymmetric vacuum in the presence of the $\Omega$-deformation. We argue that the Seiberg–Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean space $\mathbb R^4$. We conjecture the possible role of the dyonic instantons as the microscopic angular momentum carriers that could yield a spontaneous vacuum gravimagnetization. We interpret the dyonic instanton as an analogue of the Euclidean bounce in $\mathbb R^4$. Such a bounce is related to the Schwinger pair production. We also briefly discuss the induced angular momentum in $\mathbb R^4$ in the dual Liouville formulation of the $SU(2)$ theory in terms of the hypothesis of the Alday–Gaiotto–Tachikawa correspondence.