The powers of deconfinement

The trace anomaly of gluodynamics encodes the breakdown of classical scale invariance due to interactions around the deconfinement phase transition. While it is expected that at high temperatures perturbation theory becomes applicable we show that current lattice calculations are far from the perturbative regime and are dominated instead by inverse even power corrections in the temperature, while the total perturbative contribution is estimated to be extremely small and compatible with zero within error bars. We provide an interpretation in terms of dimension-two gluon condensate of the dimensionally reduced theory which value agrees with a similar analysis of power corrections from available lattice data for the renormalized Polyakov loop and the heavy quark-antiquark free energy in the deconfined phase of QCD [E. Megías, E. Ruiz Arriola and L. L. Salcedo, JHEP 0601 (2006) 073; E. Megías, E. Ruiz Arriola and L. L. Salcedo, Phys. Rev. D75 (2007) 105019].