k-String tensions and the 1/N expansion

TL;DR

This paper investigates whether k-string tensions in SU(N) gauge theories can include 1/N corrections, demonstrating that such corrections are possible and consistent with large-N expansion through specific cancellations, using strong-coupling lattice gauge theory as an example.

Contribution

The paper shows that k-string tensions can have 1/N corrections and identifies the necessary cancellations for consistency with large-N expansion, supported by a concrete lattice gauge theory example.

Findings

k-string tensions may include 1/N corrections

cancellations among Wilson loop terms ensure large-N consistency

strong-coupling lattice gauge theory confirms the theoretical analysis

Abstract

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.