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The ground state of QCD with two flavors at a finite baryon chemicalpotential under rapid rotation is a chiral soliton lattice (CSL) of the $\eta$meson, consisting of a stack of sine-Gordon solitons carrying a baryon number,due to the anomalous coupling of the $\eta$ meson to the rotation. In a largeparameter region, the ground state becomes a non-Abelian CSL, in which due tothe neutral pion condensation each $\eta$ soliton decays into a pair ofnon-Abelian sine-Gordon solitons carrying $S^2$ moduli originated fromNambu-Goldstone (NG) modes localized around it, corresponding to thespontaneously broken vector symmetry SU$(2)_{\rm V}$. There, the $S^2$ modes ofneighboring solitons are anti-aligned, and these modes should propagate in thetransverse direction of the lattice due to the interaction between the $S^2$modes of neighboring solitons. In this paper, we calculate excitationsincluding gapless NG modes and excited modes around non-Abelian and Abelian($\eta$) CSLs, and find three gapless NG modes with linear dispersion relations(type-A NG modes): two isospinons ($S^2$ modes) and a phonon corresponding tothe spontaneously broken vector SU$(2)_{\rm V}$ and translational symmetriesaround the non-Abelian CSL, respectively, and only a phonon for the Abelian CSLbecause of the recovering SU$(2)_{\rm V}$. We also find in the deconfined phasethat the dispersion relation of the isospinons becomes of the Dirac type, {\iti.~e.~} linear even at large momentum.

Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes