Nucleon mass splitting in the isospin medium

Abstract

Using the AdS/CFT correspondence, we investigate a nucleon mass splitting and pion–nucleon 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 pion–nucleon and four pion interactions which requires the modification of the known Abelian-type unitary gauge fixing because of the non-Abelian structure of the isospin medium. After finding the non-Abelian unitary gauge fixing, we find that in the isospin medium the couplings only for π0 π0 π+ π- and π0 π0π0 π0 of four pion interactions shift, while there is no pion–nucleon coupling splitting in spite of the nucleon's and meson's mass splittings.