Chiral-scale effective field theory for dense and thermal systems

In this contribution, I will present some properties of nuclear matter (NM) by using the chiral-scale effective field theory that is anchored on the chiral, scale and hidden local flavor symmetries of QCD. We show that the sound velocity (SV) of the compact star matter can saturate the conformal limit, the SV exhibits a peak configuration in the intermediate density. To extend the chiral-scale effective field theory to both dense and tnermal systems, we setup a chiral-scale density counting (CSDC) rule and explore the contributions up to $\mathcal{O}(k_c^{12})$.