  We investigate a baryon and its dilatation modes in holographic QCD based on
the Sakai-Sugimoto model, which is expressed as a 1+4 dimensional U($N_f$)
gauge theory in the flavor space. For spatially rotational symmetric systems,
we apply a generalized version of the Witten Ansatz, and reduce 1+4 dimensional
holographic QCD into a 1+2 dimensional Abelian Higgs theory in a curved space.
In the reduced theory, the holographic baryon is described as a two-dimensional
topological object of an Abrikosov vortex. We numerically calculate the baryon
solution of holographic QCD using a fine and large lattice with spacing of 0.04
fm and size of 10 fm. Using the relation between the baryon size and the
zero-point location of the Higgs field in the description with the Witten
Ansatz, we investigate a various-size baryon through this vortex description.
As time-dependent size-oscillation modes (dilatation modes) of a baryon, we
numerically obtain the lowest excitation energy of 577 MeV and deduce the
dilatational excitation of a nucleon to be the Roper resonance N$^*$(1440).
