As the first in a series of systematic work on dense hadronic matter, we study the properties of the pion in dense medium using Skyrme's effective Lagrangian as a unified theory of the hadronic interactions applicable in the large N c limit. Dense baryonic matter is described as the ground state of a skyrmion matter which appears in two differentiated phases as a function of matter density: i) at high densities as a stable cubic-centered (CC) half-skyrmion crystal; ii) at low densities as an unstable face-centered cubic (FCC) skyrmion crystal. We substitute the latter by a stable inhomogeneous phase of lumps of dense matter, which represents a naive Maxwell construction of the phase transition. This baryonic dense medium serves as a background for the pions whose effective in-medium Lagrangian we construct by allowing time-dependent quantum fluctuations on the classical dense matter field. We find that the same parameter which describes the phase transition for baryonic matter, the expectation value of the σ field, also describes the phase transition for the dynamics of the in-medium pion. Thus, the structure of the baryonic ground state crucially determines the behavior of the pion in the medium. As matter density increases, σ decreases, a phenomenon which we interpret to signal, in terms of the parameters of the effective pion Lagrangian f * π and m * π , the restoration of chiral symmetry at high density. Our calculation shows also the important role played by the higher powers in the density as it increases and chiral symmetry is being restored. This feature is likely to be generic at high density although our ground state may not be the true ground state.

We discuss the Overhauser effect ͑particle-hole pairing͒ versus the BCS effect ͑particle-particle or hole-hole pairing͒ in QCD at large quark density. In weak coupling and to leading logarithm accuracy, the pairing energies can be estimated exactly. For a small number of colors, the BCS effect overtakes the Overhauser effect, while for a large number of colors the opposite takes place, in agreement with a recent renormalization group argument. In strong coupling with large pairing energies, the Overhauser effect may be dominant for any number of colors, suggesting that QCD may crystallize into an insulator at a few times nuclear matter density, a situation reminiscent of dense Skyrmions. The Overhauser effect is dominant in QCD in 1ϩ1 dimensions, although susceptible to quantum effects. It is sensitive to temperature in all dimensions.

In continuation of our systematic effort to understand hadronic matter at high density, we study dense skyrmion matter and its chiral phase structure in an effective field theory implemented with the trace anomaly of QCD applicable in the large N c limit. By incorporating a dilaton field χ associated with broken conformal symmetry of QCD into the simplest form of skyrmion Lagrangian, we simulate the effect of "sliding vacua" influenced by the presence of matter and obtain what could correspond to the "intrinsic dependence" on the background of the system, i.e., matter density or temperature, that results when a generic chiral effective field theory of strong interactions is matched to QCD at a matching scale near the chiral scale Λ χ ∼ 4πf π ∼ 1 GeV. The properties of the Goldstone pions and the dilaton scalar near the chiral phase transition are studied by looking at the pertinent excitations of given quantum numbers on top of a skyrmion matter and their behavior in the vicinity of the phase transition from Goldstone mode to Wigner mode characterized by the changeover from the FCC crystal to the half-skyrmion CC crystal. We recover from the model certain features that are connected to Brown-Rho scaling and that suggest how to give a precise meaning to the latter in the framework of an effective field theory that is matched to QCD . 13.60.Hb, 14.70Dj