  Spontaneous symmetry breaking is studied within a simple version of the
light-front sigma model with fermions. Its vacuum structure is derived by an
implementation of global symmetries in terms of unitary operators in a finite
volume with periodic fermi field. Due to the dynamical fermion zero mode, the
vector and axial U(1) charges do not annihilate the light-front vacuum. The
latter is transformed into a continuous set of degenerate vacuum states,
leading to to the spontaneous breakdown of the axial symmetry. The existence of
associated massless Nambu-Goldstone boson is demonstrated.
