  Surface physics dominated by bulk properties has been one of the central
interests in modern condensed matter physics, from electric polarization to
bulk-boundary correspondence of topological insulators and superconductors.
Here, we extend theory of electric polarization to chirality polarizations,
that is, surface charges corresponding to local antisymmetries characterized as
a bulk property. Using the notion of chirality polarizations, we prove the
recently proposed spectral bulk-boundary correspondence, a generalization of
bulk-boundary correspondence in chiral symmetric systems into complex
frequencies. We show a physically transparent proof via Wannier functions and a
formal proof by considering the change of surface chirality charges,
highlighting the similarities and the differences between electric polarization
and chirality polarizations.
