Center vortices and k-strings

TL;DR

This paper investigates the role of center vortices in SU(N) gauge theories, analyzing their contribution to k-string tensions and scaling behaviors, and discusses implications for confinement at large N.

Contribution

It provides a detailed calculation of vortex contributions to k-string tensions and examines their scaling, challenging the vortex scenario's applicability at large N.

Findings

Surface densities grow linearly with N

Vortex scenario struggles to explain confinement at large N

Reproduces sine and Casimir scaling from lattice data

Abstract

The vortex contribution to the $k$-string tensions is computed for SU($N$) gauge theories. We deduce the surface densities needed to reproduce the sine scaling and the Casimir scaling formulae, recently obtained from numerical simulations on the lattice. We find that such densities need to grow linearly in $N$, which in turn suggests that the vortex scenario can hardly reproduce the physics of confinement at large $N$.