Gauge Dynamics And Compactification To Three Dimensions

TL;DR

This paper investigates how four-dimensional N=2 supersymmetric gauge theories behave when compactified on a circle, revealing a continuous interpolation of vacuum structures between four and three dimensions.

Contribution

It provides a detailed analysis of the vacuum structure of N=2 gauge theories on R^3 x S^1, bridging known results in four and three dimensions.

Findings

Vacuum structure varies smoothly with circle radius R.

Results agree with known three- and four-dimensional theories in respective limits.

Provides a precise characterization of the interpolation between dimensions.

Abstract

We study four dimensional $N=2$ supersymmetric gauge theories on $R^3 \times S^1$ with a circle of radius $R$. They interpolate between four dimensional gauge theories ($R=\infty$) and $N=4$ supersymmetric gauge theories in three dimensions ($R=0$). The vacuum structure can be determined quite precisely as a function of $R$, agreeing with three and four-dimensional results in the two limits.