  We study the correspondence between field theoretic and holographic dark
energy density of the universe with the modified Chaplygin gas (MCG)
respectively both in a flat and non-flat FRW universe. We present an equivalent
representation of the MCG with a homogeneous minimally coupled scalar field by
constructing the corresponding potential. A new scalar field potential is
obtained here which is physically realistic and important for cosmological
model building. In addition we also present holographic dark energy model
described by the MCG. The dynamics of the corresponding holographic dark energy
field is determined by reconstructing the potential in a non-flat universe. The
stability of the holographic dark energy in this case in a non-flat universe is
also discussed.
