Massive Gauge Theory with Quasigluon for Hot SU(N): Phase Transition and Thermodynamics

It is challenging to build a model that can correctly and unifiedly account for the deconfinement phase transition and thermodynamics of the hot $SU(N)$ pure Yang-Mills (PYM) system, for any $N$. In this article, we slightly generalize the massive PYM model to the situation with a quasigluon mass $M_g(T)$ varying with temperature, inspired by the quasigluon model. In such a framework, we can acquire an effective potential for the temporal gauge field background by perturbative calculation, rather than adding by hand. The resulting potential works well to describe the behavior of the hot PYM system for all $N$, via the single parameter $M_g(T)$. Moreover, under the assumption of unified eigenvalue distribution, the $M_g(T)$ fitted by machine learning is found to follow $N$-universality.