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We present a non-perturbative study of the equation of state in thedeconfined phase of Yang-Mills theories in D=2+1 dimensions. We introduce aholographic model, based on the improved holographic QCD model, from which wederive a non-trivial relation between the order of the deconfinement phasetransition and the behavior of the trace of the energy-momentum tensor as afunction of the temperature T. We compare the theoretical predictions of thisholographic model with a new set of high-precision numerical results fromlattice simulations of SU(N) theories with N=2, 3, 4, 5 and 6 colors. Thelatter reveal that, similarly to the D=3+1 case, the bulk equilibriumthermodynamic quantities (pressure, trace of the energy-momentum tensor, energydensity and entropy density) exhibit nearly perfect proportionality to thenumber of gluons, and can be successfully compared with the holographicpredictions in a broad range of temperatures. Finally, we also show that, againsimilarly to the D=3+1 case, the trace of the energy-momentum tensor appears tobe proportional to T^2 in a wide temperature range, starting from approximately1.2 T_c, where T_c denotes the critical deconfinement temperature.

Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II - The deconfined phase