In the pseudo-conformal phase discuused in section 2, the mass of nucleon becomes density independent and nonvanishing. It might be expected that at such a high density the chriral smmetry is getting restored with the nucleon mass decreasing or becoming zero. In the scheme of linear sigma model like Gell-Mann Levy type [
23], the finite mass of nucleon is not contradictory with the chiral symmetry, since the most part of nucleon mass is due to the spontaneous symmetry breaking of the chiral symmetry. However the nonvanishing constant nucleon mass in the pseudo-conformal phase seems not to be consistent with the chiral symmetry since the chiral codensate contribution is expected to be unimportant. The mass term in eq.(5) violates the chiral symmetry explicitly . The chiral invariance in the nucleon sector can be restored if there are excitations of the parity odd nucleons at high density. This possibility has been explored in the frame work of the parity doubling model, in which the finite mass of the nucleon can be introduced in a chiral invariant way [
11]. There can be various excitations when nucleons get closer with strong correlations. The excitations would be such the hidden symmtries of the system can be manifested. In dense hadronic matter, we consider excitations of the dilaton and the odd parity nucleons(parity partner of nucleon) for the scale symmetry and the chiral symmetry respectively. Parity doubling in dense mater is emerging as a result of the interplay betwen the scale and chiral symmetry. The relevant fields can be
and dilatons
and the parity doublet nucleon
B. The nucleon field
N in eq.(
4) is replaced by the parity doublet field
B and the mass term,
, by the parity doublet mass mass term [
24,
25] ,
where
denotes the nucleon in parity doublet in the chiral eigenstate, the
are the Pauli matrices in the parity pair space.
are dimensionless parametrs for the contribution from the spontaneousely broken chiral symmetry signified by the pion decay constant
in
.
is supposed to be from the scale symmetry breaking, where
is a mass parameter. To make eq.(
38) scale invariant we introduce two dilatons,
and
, soft and hard dilatons respectively. The soft dilaton (
) is introduced to make the spntaneous symmetry breaking part with the pion decay contant
to be scale invariant and the hard dilaton(
) for the invariant mass(
) part, the last term, to be scale invariant. Baryons
B are not mass eigenstate because of the last term. After diagonalizing the mass matrix, two mass eigen states are identified as positive parity nucleon,
, and its chiral partner,
. Their masses are given by
It is to be noted that it is a functional of dialtons such that it transforms as scale dimension 1. In a linearized scheme suitable for the study of dynamical aspects of chiral symmetry, the vacuum expectation value of scalar field ,
in Gell-Mann Levy type model, becomes zero at chiral symmetry restoration,
which corresponds to the dilaton limit [
26] in which
-nucleon coupling is supposed to be no longer active. The nucleon mass becomes
.
A part of nucleon mass is generated by dynamically via spontaneous symmetry breaking of the chiral symmetry. The rest of the nucleon mass up to 70 % is unconnected with the chiral symmetry breaking. It is supposed to be the contribution from the spontaneous symmetry breaking of the scale symmetry. The excitation of parity doublets in the compact star matter makes these features in its mass formula compatible with the chiral symmetry. The parity doubling is one of the emergent phenomena in the pseudo-conformal phase of strongly correlated dense compact star matter.