k-String Tensions and Center Vortices at Large N

TL;DR

This paper explains the Casimir/Sine Law scaling of k-string tensions at large N using the center vortex mechanism, highlighting the role of Z(N) monopoles and vortex stability across various lattice actions.

Contribution

It provides a natural explanation for k-string tension scaling at large N via center vortices and extends the stability of vortices to a broad class of lattice actions.

Findings

Center vortices explain k-string tension scaling at large N.

Vortex densities do not grow with N, avoiding pathologies.

Center vortices are stable solutions for N>4 across various lattice actions.

Abstract

We point out that there is a natural explanation, in terms of the center vortex confinement mechanism, for the expected Casimir/Sine Law scaling of k-string tensions in the large N limit. The crucial ingredient is the existence of Z(N) center monopoles, which go over to U(1) monopoles in this limit. Vortex densities leading to Casimir/Sine Law scaling at large-N are constructed; these densities have no obvious pathologies and in particular do not grow with N. We also note that center vortices are stable classical solutions of the Wilson action, for all SU(N) gauge theories with N>4, and extend this old result to a broad class of lattice actions motivated by the improved action program and the renormalization group.