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

TL;DR

This paper combines holographic modeling and lattice simulations to analyze the thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions, revealing proportionality of thermodynamic quantities to gluon number and T^2 behavior of the trace tensor.

Contribution

It introduces a holographic model for 2+1D Yang-Mills theories and validates it with high-precision lattice data across multiple N values.

Findings

Thermodynamic quantities scale with the number of gluons.

Trace of energy-momentum tensor is proportional to T^2 above 1.2 T_c.

Holographic predictions match lattice results over a broad temperature range.

Abstract

We present a non-perturbative study of the equation of state in the deconfined phase of Yang-Mills theories in D=2+1 dimensions. We introduce a holographic model, based on the improved holographic QCD model, from which we derive a non-trivial relation between the order of the deconfinement phase transition and the behavior of the trace of the energy-momentum tensor as a function of the temperature T. We compare the theoretical predictions of this holographic model with a new set of high-precision numerical results from lattice simulations of SU(N) theories with N=2, 3, 4, 5 and 6 colors. The latter reveal that, similarly to the D=3+1 case, the bulk equilibrium thermodynamic quantities (pressure, trace of the energy-momentum tensor, energy density and entropy density) exhibit nearly perfect proportionality to the number of gluons, and can be successfully compared with the holographic predictions in a broad range of temperatures. Finally, we also show that, again similarly to the D=3+1 case, the trace of the energy-momentum tensor appears to be proportional to T^2 in a wide temperature range, starting from approximately 1.2 T_c, where T_c denotes the critical deconfinement temperature.