k-String tensions and their large-N dependence

TL;DR

This paper investigates the N-dependence of k-string tensions, demonstrating that odd powers of 1/N can be compatible with large-N expansion through specific cancellations, challenging previous assumptions.

Contribution

It shows that k-string tensions can have leading 1/N corrections without violating large-N expansion, using strong coupling lattice gauge theory as an example.

Findings

k-string tensions may include odd powers of 1/N

pairwise cancellations ensure consistency with large-N expansion

Casimir scaling observed in strong coupling lattice gauge theory

Abstract

We consider whether the 1/N corrections to k-string tensions must begin at order 1/N^2, as in the Sine Law, or whether odd powers of 1/N, as in Casimir Scaling, are also acceptable. The issue is important because different models of confinement differ in their predictions for the representation-dependence of k-string tensions, and corrections involving odd powers of 1/N would seem to be ruled out by the large-N expansion. We show, however, that k-string tensions may, in fact, have leading 1/N corrections, and consistency with the large-N expansion, in the open string sector, is achieved by an exact pairwise cancellation among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations come about in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action, in which k-string tensions follow the Casimir scaling rule.