$k$ Strings from Various Perspectives: QCD, Lattices, String Theory and Toy Models

TL;DR

This paper reviews the current understanding of k-string tensions in Yang-Mills theory, explores a toy model for QCD strings, and presents new results supporting the sine formula in a two-dimensional model.

Contribution

It introduces a weakly coupled 4D Yang-Mills toy model with non-Abelian strings and provides original evidence for the sine formula in a 2D toy model.

Findings

Support for the sine formula in 2D toy models

Analysis of k-string tensions in Yang-Mills theory

Proposal of a toy model for QCD strings

Abstract

I review the status of the issue of the k-string tension in Yang-Mills theory. After a summary of known facts I discuss a weakly coupled four-dimensional Yang-Mills theory that supports non-Abelian strings and can, in certain aspects, serve as a toy model for QCD strings. In the second part of the talk I present original results obtained in a two-dimensional toy model which provides some evidence for the sine formula.