all processes involved, avoiding mixing different models for different steps. Furthermore one should express the spectral function in terms of variables that track the chiral property of the system in terms of the order parameter, i.e., the quark condensate.

HLS$_1$ theory provides one such framework, with its local gauge invariance enabling one to access the vector fields whose mass scale can drop as low as that of the pion near the critical point.

The theoretical ingredients necessary within the framework of HY’s HLS$_1$ theory were spelled out in two unpublished articles [@BR:NA60]. They are (1) the intrinsic background (temperature, density) dependence demanded by matching to QCD [@HY:PR], (2) the violation of the vector dominance in the pion EM form factor in hot and/or dense medium that results from the vector manifestation of chiral symmetry in the HLS/VM theory [@HS:VD] and (3) many-body correlations generated by the presence of the Fermi surface, which may be considered as a quantum critical phenomenon [@BHLR06].

In order to implement all three ingredients in a consistent way, baryonic degrees of freedom are mandatory. In HLS$_\infty$ theory, they are skyrmions in an infinite tower of vector mesons if viewed in four dimensions. No such formulation exists 