Center-Vortex Solutions of the Yang-Mills Effective Action in Three and Four Dimensions

TL;DR

This paper calculates the one-loop effective action for SU(2) Yang-Mills center-vortex configurations in 3D and 4D, finding minima indicating potential vacuum instability due to vortex formation.

Contribution

It provides the first calculation of the effective action for center-vortex configurations in both three and four dimensions, revealing possible vacuum instability.

Findings

Minima of the effective action correspond to specific vortex sizes.

Effective action minima are negative, indicating potential vacuum instability.

Vortex sizes are approximately 4/g_3^2 in 3D and 1.7/Lambda_MS in 4D.

Abstract

We calculate the one-loop effective action of the SU(2) Yang-Mills theory for center-vortex configurations, both in 3d and 4d. We find that in both cases there are minima of the effective action, corresponding to vortices of the transverse size approximately 4/g_3^2 and 1.7/Lambda_MS, respectively. The values of the effective actions at the minima are negative, suggesting that the Euclidian vacuum may be unstable with respect to creation of vortices.