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We discuss the dispersionless spectrum with zero energy in the lineartopological defects - vortices. The flat band emerges inside the vortex livingin the bulk medium containing topologically stable Fermi points in momentumspace. The boundaries of the flat band in the vortex are determined byprojections of the Fermi points in bulk to the vortex axis. This bulk-vortexcorrespondence for flat band is similar to the bulk-surface correspondencediscussed earlier in the media with topologically protected lines of zeroes. Inthe latter case the flat band emerges on the surface of the system, and itsboundary is determined by projection of the bulk nodal line on the surface.

Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points