  We study the baryon vertex (BV) in the presence of medium using DBI action
and the force balance condition between BV and the probe branes. We note that a
stable BV configuration exists only in some of the confining backgrounds. For
the system of finite density, the issue is whether there is a canonical
definition for the baryon mass in the medium. In this work, we define it as the
energy of the deformed BV satisfying the force balance condition (FBC) with the
probe brane. With FBC, lengths of the strings attached to the BV tend to be
zero while the compact branes are enlongated to mimic the string. We attribute
the deformation energy of the probe brane to the baryon-baryon interaction. We
show that for a system with heavy quarks the baryon mass drops monotonically as
a function of density while it has minimum in case of light quark system.
