Worldsheet theory of the confining flux tube at large N
In plain words
The tube of gluon field between quarks vibrates like a string, and lattice simulations of its vibrations show an extra particle living on the string, called the worldsheet axion. Which exact theory lives on the string as the number of colors grows is unknown.
Precise statement
Lattice spectra of closed flux tubes in 4D $\mathrm{SU}(N)$ Yang-Mills ($N = 3, 5, 6$) are fitted by an effective string of two transverse phonons plus a massive pseudoscalar worldsheet axion coupled to the phonons through a topological term (Dubovsky, Flauger, Gorbenko 2013; Athenodorou, Dubovsky, Luo, Teper 2024). Determine the $N \to \infty$ limits of the axion mass $m_a/\sqrt{\sigma}$ and its coupling, and whether the large-N worldsheet theory is the integrable axionic string constructed by Dubovsky and Gorbenko (2015).
What would settle it
Large-$N$ extrapolation of lattice flux-tube spectra for $N$ up to about 10, combined with $S$-matrix bootstrap bounds on worldsheet scattering, fixing $m_{a}/\sqrt{\sigma}$ and the axion coupling at $N = \infty$.
Status in the literature
Unverified note
Lattice data for $N = 3, 5, 6$ (Athenodorou, Dubovsky, Luo, Teper 2024, arXiv:2411.03435) fit the phonon plus massive axion effective theory; the large-$N$ limit of the axion parameters is not established.