The trace anomaly or, equivalently, the interaction measure is an important thermodynamic quantity/observable, since it is very sensitive to the non-perturbative effects in the gluon plasma. It has been calculated and its analytic and asymptotic properties have been investigated with the combined force of analytic and lattice approaches to the [Formula: see text] Yang-Mills (YM) quantum gauge theory at finite temperature. The first one is based on the effective potential approach for composite operators properly generalized to finite temperature. This makes it possible to introduce into this formalism a dependence on the mass gap [Formula: see text], which is responsible for the large-scale dynamical structure of the QCD ground state. The gluon plasma pressure as a function of the mass gap adjusted by this approach to the corresponding lattice data is shown to be a continuously growing function of temperature [Formula: see text] in the whole temperature range [Formula: see text] with the correct Stefan-Boltzmann limit at very high temperature. The corresponding trace anomaly has a finite jump discontinuity at some characteristic temperature [Formula: see text] with latent heat [Formula: see text]. This is a firm evidence of the first-order phase transition in [Formula: see text] pure gluon plasma. It is exponentially suppressed below [Formula: see text] and has a complicated and rather different dependence on the mass gap and temperature across [Formula: see text]. In the very high temperature limit its non-perturbative part has a power-type fall off.
On the trace anomaly and the anomaly puzzle in $ \mathcal{N} = 1 $ pure Yang-Mills
