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The Polyakov loop dependence of bulk viscosity of QCD matter

In this work, we show the dependence of bulk viscosity on Polyakov loop in 3+1 dimensional topologically massive model (TMM). This model contains equally massive non-Abelian gauge fields without spontaneous symmetry breaking. In earlier works, the bulk viscosity was found from the trace anomaly in massless $ϕ^4$ model and Yang-Mills (YM) theory and its dependence on the quantum corrections was established. In TMM, the trace anomaly is absent due to the presence of kinetic term of a two-form field $B$ in the action. This model also provides the dependence of bulk viscosity on the mass of the gauge bosons. The mass of the gauge bosons in TMM acts as magnetic mass in the perturbative thermal field theory. This magnetic mass is gauge independent unlike what is found in massless YM theory. The ratio of bulk viscosity and entropy density vs temperature is plotted which shows the required behaviour near critical point. We also observe that the strong coupling constant has the same behaviour at high energy limit (i.e. asymptotic freedom) as that of massless YM theory at zero temperature.