The worldvolume fermion as baryon in holographic QCD with instanton

In this work, we investigate the worldvolume fermion on the flavor brane in the D0-D4/D8 model which is holographically equivalent to the four-dimensional QCD with instantons, or equivalently with a theta angle. The action for the worldvolume fermion is obtained by the T-duality rules in string theory and we accordingly derive its effectively five-dimensional, canonical four-dimensional forms by using the systematical dimensional reduction and decomposition of spinor. Afterwards, we employ the AdS/CFT dictionary in order to evaluate the two-point correlation function as the spectral function for the worldvolume fermion and interpret the fermion as baryon by analyzing its quantum number with the baryon vertex in holography. In this sense, the interacted action involving the worldvolume fermion and gauge field on the flavor brane are finally derived in holography which describes the various interaction of meson and baryon with instantons in large-N limit. Therefore, this work provides a holographic picture to describe baryon and its interactions based on string theory, in particular, in the presence of instantons or a theta angle.