Non-Abelian Strings and the Luscher Term

TL;DR

This paper calculates the Luscher term for non-Abelian strings in gauge theories, revealing a dependence on the gauge group rank and showing a transition in the Luscher coefficient related to string length scales.

Contribution

It provides a novel calculation of the Luscher term for non-Abelian strings, highlighting the influence of orientational zero modes and gauge group rank on the string's quantum corrections.

Findings

Luscher term for non-Abelian strings is Nπ/12, depending on gauge group rank.

The Luscher coefficient transitions from Nπ/12 to π/12 as string length increases.

The study raises questions about additional light moduli on QCD string worldsheets at large N.

Abstract

We calculate the Luscher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian subgroup. The Luscher term is determined by the number of light degrees of freedom on the string wordsheet. Unlike the standard \pi/12 we get N\pi/12 for non-Abelian strings in the U(N) gauge theories. Thus, the Luscher coefficient acquires a dependence on the rank of the gauge group. In the models with non-Abelian strings discussed in the literature there are two distinct scales: the string tension \xi (the string thickness \sim \xi^{-1/2}) and the dynamical scale of strong interactions \Lambda. At weak coupling \xi\gg\Lambda^2. The Luscher term for non-Abelian strings experiences a jump: at \xi^{-1/2}\ll L\ll \Lambda^{-1} it is N\pi/12 while at at L\gg \Lambda^{-1} the orientational moduli are frozen out and the Luscher coefficient approaches its "Luscher" value \pi/12. We raise the question of possible extra (i.e. non-translational) light moduli on the worldsheet of QCD strings at large N.