Chiral symmetry and scale invariance in the equation of state of strongly interacting matter

We present an equation of state for strongly interacting matter aimed at exploring its thermodynamic behavior over a wide range of temperatures and baryon densities. Going beyond the standard mean-field approximation, the equation of state is derived from an effective Lagrangian of nucleons and mesons (σ, π, ω, ρ), with thermal field fluctuations systematically incorporated.
A key feature of the framework is its consistent treatment of fundamental symmetries: it accounts for explicitly broken chiral symmetry and spontaneously broken scale invariance, with the latter governed by the dynamics of a dilaton field. After validating the role of thermal field fluctuations against lattice QCD results in the pure-gauge SU(3)_c sector, we extend the analysis to the hadronic sector at finite temperature and baryon chemical potential.
The resulting QCD phase diagram exhibits chiral symmetry restoration, appearing as a crossover at high temperature and evolving into a first-order phase transition at high baryon density. At the same time, the dilaton field induces a robust first-order transition associated with the restoration of scale symmetry. Finally, we implement this microphysically motivated equation of state to model compact astrophysical objects, evaluating the macroscopic structure, mass–radius relations, tidal deformabilities, and internal thermodynamics of both cold neutron stars and hot proto-neutron stars.