  Dynamical nature of the gauge degree of freedom and its effect to fermion
spectrum are studied at $\beta=\infty$ for two-dimensional nonabelian chiral
gauge theory in the vacuum overlap formulation. It is argue that the disordered
gauge degree of freedom does not necessarily cause the massless chiral state in
the (waveguide) boundary correlation function. An asymptotically free
self-coupling for the gauge degree of freedom is introduced by hand at first.
This allows us to tame the gauge fluctuation by approaching the critical point
of the gauge degree of freedom without spoiling its disordered nature. We
examine the spectrum in the boundary correlation function and find the mass gap
of the order of the lattice cutoff. There is no symmetry against it. Then we
argue that the decoupling of the gauge freedom can occur as the self-coupling
is removed, provided that the IR fixed point due to the Wess-Zumino term is
absent by anomaly cancellation.
