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

TL;DR

This paper explores the relationship between the Seiberg-Witten prepotential and vacuum angular momentum in ${ m N}=2$ SYM theory within the $ ext{Omega}$-background, proposing dyonic instantons as key angular momentum carriers.

Contribution

It introduces a novel connection between the Seiberg-Witten prepotential and vacuum gravimagnetization, and suggests dyonic instantons as microscopic angular momentum sources.

Findings

Seiberg-Witten prepotential relates to vacuum angular momentum density.

Dyonic instantons may induce spontaneous gravimagnetization.

Dual Liouville theory offers an alternative perspective on angular momentum.

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.