Confining strings in representations with common $n$-ality

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.