We review an approach, developed over the past few years, to describe hadronic matter at finite density and temperature, whose underlying theoretical framework is the Skyrme model, an effective low energy theory rooted in large Nc QCD. In this approach matter is described by various crystal structures of skyrmions, classical topological solitons carrying baryon number, from which conventional baryons appear by quantization. Chiral and scale symmetries play a crucial role in the dynamics as described by pion, dilaton and vector meson degrees of freedom. When compressed or heated skyrmion matter describes a rich phase diagram which has strong connections with the confinement/deconfinement phase transition. IntroductionAn important issue at present is to understand the properties of hadronic matter under extreme conditions, e.g., at high temperature as in relativistic heavy-ion physics and/or at high density as in compact stars. The phase diagram of hadronic matter turns out richer than what has been predicted by perturbative Quantum Chromodynamics (QCD).1 Two approaches have been developed thus far to discuss this issue : on the one hand, Lattice QCD which deals directly with quark and gluon degrees of freedom, and on the other, effective field theories which are described in terms of hadronic fields. We shall describe in here a formalism for the second approach based on the topological soliton description of hadronic matter firstly introduced by Skyrme. 2,3Lattice QCD, the main computational tool accessible to highly nonperturbative QCD, has provided much information on the the finite temperature transition, such as the value of the critical temperature, the type of equation of state, etc.
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