  We propose a mechanism of topology-induced symmetry breaking, where certain
local symmetry preserved by the Hamiltonian is broken in the excited
eigenstates due to the nontrivial boundary condition. As a demonstration, we
study magnon excitations on a M\"obius strip comprising of two
antiferromagnetically coupled spin chains. Even under a simple Hamiltonian
respecting local rotational symmetry and without considering curvature effects,
magnons exhibit linear polarization of the N\'eel vector devoid of chirality
and form two non-degenerate branches that cannot be smoothly connected to or be
decomposed by the circularly-polarized magnons typically seen in
antiferromagnets. One branch supports standing-wave formation on the M\"obius
strip while the other does not, owing to its spectral shift incurred by the
boundary condition. Our findings showcase the significant influence of
real-space topology on the physical nature of quasiparticles.
