instance the axial vector meson $a_1$ etc. This gives a $bare$ Lagrangian whose parameters are given by QCD variables such as the strong coupling constant $\alpha_s$, the quark condensate $\la\bar{q}q\ra$, the gluon condensate $\la
G^2_{\mu\nu}\ra$ etc. Quantum calculations are done with the bare HLS Lagrangian so determined by renormalization group equations.

An important point to note here: [*Since the condensates in the QCD sector are background-dependent, that is, dependent on temperature, density etc, the bare Lagrangian HLS$_1$ is endowed with “intrinsic (background) dependence."*]{}

The fixed point of HLS$_1$
--------------------------

In the chiral limit and with $V_1=\rho$, there are three parameters in the HLS$_1$ Lagrangian, $g$, $F_\pi$ and $a$ where $g$ is the gauge coupling constant of HLS$_1$, $F_\pi$ is the parametric pion decay constant [^5] and $a=(F_\sigma/F_\pi)^2$ figuring in the chiral fields (\[chifields\]). Harada and Yamawaki showed that the RGEs for these parameters have the fixed point consistent with QCD [^6] g\^\*=0,  a\^\*=1.\[fixed\] This was explicitly shown to one-loop order but one can readily convince oneself that it should hold to all loop orders. This fixed point dictates how the hadronic system makes a phase transition from the chiral symmetry broken phase to the restored phase. [*The fixed point (\[fixed\]) 