Linear growth of the trace anomaly in Yang-Mills thermodynamics

In the lattice work by Miller and in the work by Zwanziger a linear growth of the trace anomaly for high temperatures was found in pure SU(2) and SU(3) Yang-Mills theories. While future numerical work is needed to confirm or to rule out the linear growth, the aforementioned results point to the remarkable property that the corresponding systems are strongly interacting even at high temperatures. We show that within an analytical approach to Yang-Mills thermodynamics this linear rise is obtained and is directly connected to the presence of a temperature-dependent ground state, which describes (part of) the nonperturbative nature of the Yang-Mills system. Our predictions are in approximate agreement with Miller and Zwanziger.

Figure 1

The quantities $\frac{{\theta }_{\mu \mu }}{{\Lambda }^4}$ (left panel, gray curve: large-$T$ behavior; black curve: finite-$T$ behavior) and $h$ (right panel) as functions of $\frac{\lambda }{{\lambda }_c}=\frac{T}{T_c}$ in the case of SU(2).

Figure 2

Scaled energy density $\rho$ (black), pressure $p$ (dark gray), and entropy density $s$ (light gray) in the deconfining phase of SU(2) Yang-Mills thermodynamics.