Connecting dilaton thermal fluctuation with the Polyakov loop at finite temperature

A bstract Understanding the character of the deconfinement phase transition is one of the fundamental challenges in particle physics. In this work, we derive a formula for the expectation value of the Polyakov loop — the order parameter of the deconfinement phase transition — in pure SU(N c ) gauge systems at finite temperature starting from the Coleman–Weinberg-type effective potential encoding the trace anomaly of QCD. Our results are in good agreement with the Lattice QCD data and can effectively describe the large- N c behaviors of the expectation value of the Polyakov loop. Notably, our findings predict the strongest first-order deconfinement phase transition as N c → + ∞ . Furthermore, to establish a relation between the dilaton field and the Polyakov loop, we also derive the scale transformation rule for temperature based on quantum statistical mechanics. The results of this work may shed a light on the connection between deconfinement phase transition and evolution of scale symmetry in the thermal system.