Angular Momentum and Gravimagnetization of the ${\cal N}=2$ SYM vacuum

Abstract

In this note we discuss the gravimagnetization of the ${\cal N}=2$ SYM vacuum in the $\Omega$-background. It is argued that the Seiberg-Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean $R^4$ space. The possible role of the dyonic instantons as the microscopic angular momentum carriers which could yield the spontaneous vacuum gravimagnetization is conjectured. We interpret the dyonic instanton as a kind of the Euclidean bounce in $R^4$ similar to one responsible for the Schwinger pair creation. The induced angular momentum in $R^4$ is also briefly considered in the dual Liouville formulation of $SU(2)$ theory via AGT relation.