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

Abstract

A simple holographic model is presented and analyzed that describes chiral symmetry breaking and the physics of the meson sector in QCD. This is a bottom-up model that incorporates string theory ingredients like tachyon condensation which is expected to be the main manifestation of chiral symmetry breaking in the holographic context. As a model for glue the Kuperstein-Sonnenschein background is used. The structure of the flavor vacuum is analyzed in the quenched approximation. Chiral symmetry breaking is shown at zero temperature. Above the deconfinement transition chiral symmetry is restored. A complete holographic renormalization is performed and the chiral condensate is calculated for different quark masses both at zero and non-zero temperatures. The 0 ++ , 0 −+ , 1 ++ , 1 −− meson trajectories are analyzed and their masses and decay constants are computed. The asymptotic trajectories are linear. The model has one phenomenological parameter beyond those of QCD that affects the 1 ++ , 0 −+ sectors. Fitting this parameter we obtain very good agreement with data. The model improves in several ways the popular hard-wall and soft wall bottom-up models.

Matrix model for deconfinement in aSU(2)gauge theory in2+1dimensions

“…[10]. We show the plots for the pressure, the interaction measure, and for the Polyakov loop utilizing three different options for the q-dependent nonperturbative term ∼ C 1 : the linear term, Close to the critical temperature the lattice data become smeared out due to glueballs below T d , the gluon mass above T d , and lattice artifacts such as finite-volume effects.…”

“…The numerical results for the pressure and for the interaction measure are presented and compared to the lattice data of Ref. [10].…”

“…Taking this into account, one must certainly add a constant term ∼ T 2 d T 2 . For the pressure, this is the dominant term for temperatures above [6,10], one must also add a constant nonperturbative term ∼ T d T 2 to the potential for q.…”

“…is approximately constant [6,10]. Second, it is natural to include a term similar to that generated in perturbation theory, Eq.…”

“…The interaction measure in three dimensions, [e(T ) − 2p(T )] /T 3 , times a single power [6,10]. This implies that in this region, the pressure is dominated by a constant term ∼ T 2 T d .…”