Closed flux tubes in higher representations and their string description in D=2+1 SU(N) gauge theories

TL;DR

This study numerically investigates the spectrum of closed flux tubes in various representations of SU(N) gauge theories in 2+1 dimensions, finding that ground states align with Nambu-Goto predictions while excited states show significant deviations.

Contribution

It provides the first detailed numerical analysis of flux tubes in higher representations, demonstrating their existence and comparing their spectra to string models in SU(N) gauge theories.

Findings

Ground states match Nambu-Goto string spectrum.

Excited states deviate significantly from string predictions.

Flux tubes in higher representations are confirmed to exist.

Abstract

We calculate, numerically, the low-lying spectrum of closed confining flux tubes that carry flux in different representations of SU(N). We do so for SU(6) at beta=171, where the calculated low-energy physics is very close to the continuum limit and, in many respects, also close to N=infinity. We focus on the adjoint, 84, 120, k=2A,2S and k=3A,3M,3S representations and provide evidence that the corresponding flux tubes, albeit mostly unstable, do in fact exist. We observe that the ground state of a flux tube with momentum along its axis appears to be well defined in all cases and is well described by the Nambu-Goto free string spectrum, all the way down to very small lengths, just as it is for flux tubes carrying fundamental flux. Excited states, however, typically show very much larger deviations from Nambu-Goto than the corresponding excitations of fundamental flux tubes and, indeed, cannot be extracted in many cases. We discuss whether what we are seeing here are separate stringy and massive modes or simply large corrections to energy levels that will become string-like at larger lengths.