Remarks on Stable and Quasi-stable k-Strings at Large N

TL;DR

This paper analyzes the properties of stable and quasi-stable k-strings in large-N Yang-Mills theories, clarifying their tensions, decay rates, and the theoretical formulas governing their behavior, with implications for lattice simulations.

Contribution

It introduces a systematic approach to understanding quasi-stable strings at large N and clarifies their decay mechanisms and tension dependencies, contrasting with previous lattice reports.

Findings

Quasi-stable strings decay with suppressed rates at large N.

String tension depends only on N-ality for stable strings.

Arguments favoring the sine formula over the Casimir formula.

Abstract

We discuss k-strings in the large-N Yang-Mills theory and its supersymmetric extension. Whereas the tension of the bona fide (stable) QCD string is expected to depend only on the N-ality of the representation, tensions that depend on specific representation R are often reported in the lattice literature. In particular, adjoint strings are discussed and found in certain simulations. We clarify this issue by systematically exploiting the notion of the quasi-stable strings which becomes well-defined at large N. The quasi-stable strings with representation-dependent tensions decay, but the decay rate (per unit length per unit time) is suppressed as Lambda^2 F(N) where F(N) falls off as a function of N. It can be determined on the case-by-case basis. The quasi-stable strings eventually decay into stable strings whose tension indeed depends only on the N-ality. We also briefly review large-N arguments showing why the Casimir formula for the string tension cannot be correct, and present additional arguments in favor of the sine formula. Finally, we comment on the relevance of our estimates to Euclidean lattice measurements.