  We discuss the dispersionless spectrum with zero energy in the linear
topological defects - vortices. The flat band emerges inside the vortex living
in the bulk medium containing topologically stable Fermi points in momentum
space. The boundaries of the flat band in the vortex are determined by
projections of the Fermi points in bulk to the vortex axis. This bulk-vortex
correspondence for flat band is similar to the bulk-surface correspondence
discussed earlier in the media with topologically protected lines of zeroes. In
the latter case the flat band emerges on the surface of the system, and its
boundary is determined by projection of the bulk nodal line on the surface.
