We present a major update on the spectrum of the closed flux-tube (torelon) in D = 3 + 1 SU (N ) gauge theories. Namely, we calculate the excitation spectrum of a confining flux-tube which winds around a spatial torus as a function of its length l, for short as well as long tubes. We do so for N = 3, 5, 6 and two different values of the lattice spacing. Our states are characterised by the quantum numbers of spin J, transverse parity P ⊥ , longitudinal parity P as well as by the longitudinal momentum p . Our extended basis of operators used in combination with the generalized eigenvalue method enables us to extract masses for all irreducible representations characterised by {|J|, P ⊥ , P }. We confirm that most of the low-lying states are well described by the spectrum of the Goddard-Goldstone-Rebbi-Thorn string. In addition we provide strong evidence, that in addition to string like states, massive modes exist on the world-sheet. More precisely the ground state with quantum numbers |J| P ⊥ ,P = 0 −− exhibits a behaviour which is in agreement with the interpretation of being an axion on the world-sheet of the flux-tube. This state arises from a topological interaction term included in the effective world-sheet action. In addition we observe that the second excited state with |J| P ⊥ ,P = 0 ++ behaves as a massive mode with mass twice that of the axion.