Nucleon mass splitting in the isospin medium

Using the AdS/CFT correspondence, we investigate a nucleon mass splitting and nucleon-pion coupling in the isospin medium. We find that there exists a nucleon mass splitting which is exactly given by the half of the meson mass splitting because nucleon has the half isospin charge of the charged mesons. In addition, we also investigate the nucleon-pion coupling, which requires the modification of the known Abelian-type unitary gauge fixing term because non-Abelian fluctuations should be taken into account in the isospin medium. In this paper, after constructing an appropriate unitary gauge fixing term, we find that in spite of the nucleon's and meson's mass splittings, there is no nucleon-pion coupling splitting in the isospin medium.