In this study, we conduct a thorough examination of the spectrum of the open confining string in $3+1$ dimensions, commonly referred to as the open flux tube, across various gauge groups of $SU(N_c)$. Our primary objective is to explore its behavior as we approach the large-$N_c$ limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for $N_c=3$, 4, 5, 6. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large-$N_c$ limit. More specifically, we analyze the spectra of flux tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum $\mathrm{\Lambda }$, charge conjugation and parity ${\eta }_{CP}$, and the reflection symmetry $\epsilon$ for $\mathrm{\Lambda }=0$. To this purpose we employ a diverse set of suitable operators, an anisotropic action, and smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axionlike state along the flux-tube world sheet. Notably, we provide undoubted evidence of the existence of a massive axionlike particle with the same mass as the corresponding axion extracted within the context of closed flux tube. This strengthens the conjecture that the axion is a property of the world sheet of the QCD string.

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• Color confinement
• Lattice field theory
• Quantum chromodynamics
• Quantum field theory
• String phenomenology