Closed flux tubes in D=2+1 SU(N) gauge theories: dynamics and effective string description

TL;DR

This paper investigates the spectrum of closed flux tubes in 2+1 dimensional SU(N) gauge theories, providing new insights into effective string corrections, world-sheet excitations, and flux tube interactions across different N values.

Contribution

It offers new calculations of flux tube spectra in SU(4) and SU(8), demonstrating the power-law correction order and exploring the role of massive world sheet modes across various SU(N) groups.

Findings

Leading non-universal correction exponent gamma ≥ 7.

Massive world sheet excitations reflect the bulk theory's group structure.

Flux tubes in different representations are nearly orthogonal, indicating suppressed gluon screening.

Abstract

We extend our earlier calculations of the spectrum of closed flux tubes in SU(N) gauge theories in 2+1 dimensions, with a focus on questions raised by recent theoretical progress on the effective string action of long flux tubes and the world-sheet action for flux tubes of moderate lengths. Our new calculations in SU(4) and SU(8) provide evidence that the leading O(1/l^gamma) non-universal correction to the flux tube ground state energy does indeed have a power gamma greater than or equal to 7. We perform a study in SU(2), where we can traverse the length at which the Nambu-Goto ground state becomes tachyonic, to obtain an all-N view of the spectrum. Our comparison of the k=2 flux tube excitation energies in SU(4) and SU(6) suggests that the massive world sheet excitation associated with the k=2 binding has a scale that knows about the group and hence the theory in the bulk, and we comment on the potential implications of world sheet massive modes for the bulk spectrum. We provide a quantitative analysis of the surprising (near-)orthogonality of flux tubes carrying flux in different SU(N) representations, which implies that their screening by gluons is highly suppressed even at small N.