Center Vortices at N > 4 Colors

TL;DR

This paper explores the stability of center vortices in SU(N) gauge theories for N > 4 and discusses how the vortex model explains the scaling of k-string tensions at large N, emphasizing the role of center monopoles.

Contribution

It demonstrates that center vortices are stable classical solutions for N > 4 and clarifies the scaling behavior of k-string tensions in the vortex picture of confinement.

Findings

Center vortices are stable solutions for N > 4.

The scaling of k-string tensions is linear in k at large N.

Center monopoles are crucial for the observed scaling behavior.

Abstract

We discuss two issues related to the physics of center vortices in pure SU(N) lattice gauge theory at large N: (1) Center vortices are stable classical solutions of the Wilson action, as well as of a wide class of improved lattice actions, for any N > 4. (2) The natural scaling of k-string tensions at large N, in the vortex picture of confinement, is \sigma(k)=k \sigma(1). This is the common large N limit of Casimir and Sine Law scaling. The crucial feature for explaining this behavior is the existence of center monopoles.