Confining strings in representations with common $n$-ality

TL;DR

This paper uses lattice Monte Carlo simulations to study confining strings in SU(3) gauge theory, confirming that their spectrum aligns with predictions based on $n$-ality and Casimir scaling, especially in the rank-2 symmetric channel.

Contribution

It provides the first direct lattice evidence that the confining string spectrum matches $n$-ality predictions and demonstrates the two-exponential structure of torelon correlations in different representations.

Findings

String spectrum agrees with $n$-ality predictions.

The ratio of string tensions matches Casimir scaling (5/2).

Torelon correlations are well described by a two-exponential model.

Abstract

We study the spectrum of confining strings in SU(3) pure gauge theory, by means of lattice Monte Carlo simulations, using torelon operators in different representations of the gauge group. Our results provide direct evidence that the string spectrum is according to predictions based on $n$-ality. Torelon correlations in the rank-2 symmetric channel appear to be well reproduced by a two-exponential picture, in which the lowest state is given by the fundamental string $\sigma_1=\sigma$, the heavier string state is such that the ratio $\sigma_2/\sigma_1$ is approximately given by the Casimir ratio $C_{\rm sym}/C_{\rm f} = 5/2$, and the torelon has a much smaller overlap with the lighter fundamental string state.