Chiral Restoration in Hot and/or Dense Matter

Chiral restoration phase transition in hot and/or dense hadronic matter is discussed in terms of the BR scaling based on chiral symmetry and scale anomaly of QCD. The precise connection between the scalar field that figures in the trace anomaly and the sigma field that figures in the linear $\sigma$ model is established. It is suggested that in hot and/or dense medium, the nonlinear $\sigma$ model linearizes with the help of a dilaton to a linear $\sigma$ model with medium-renormalized constants. The relevance of Georgi's vector symmetry and/or Weinberg's ``mended symmetry" in chiral restoration is pointed out. Some striking consequences for relativistic heavy-ion collisions and dense matter in compact stars following stellar collapse are discussed.Comment: 66 pages, Latex, 19 figures (not included, available on request), Prepared for Physics Report