On the Vacuum energy of a Color Magnetic Vortex

TL;DR

This paper computes the one-loop gluon vacuum energy in the presence of a color magnetic vortex for SU(2) and SU(3), revealing intrinsic instability due to tachyonic modes.

Contribution

It provides analytic expressions for vacuum energy using zeta regularization and investigates the stability of various vortex profiles.

Findings

Vacuum energy is positive and increases with profile variations.

All profiles studied exhibit tachyonic modes, indicating instability.

The method allows for numerical evaluation of vortex energies.

Abstract

We calculate the one loop gluon vacuum energy in the background of a color magnetic vortex for SU(2) and SU(3). We use zeta functional regularization to obtain analytic expressions suitable for numerical treatment. The momentum integration is turned to the imaginary axis and fast converging sums/integrals are obtained. We investigate numerically a number of profiles of the background. In each case the vacuum energy turns out to be positive increasing in this way the complete energy and making the vortex configuration less stable. In this problem bound states (tachyonic modes) are present for all investigated profiles making them intrinsically unstable.