Universal relaxation in quark-gluon plasma at strong coupling

We use top-down gauge theory/string theory correspondence to compute relaxation rates in strongly coupled nonconformal gauge theory plasma. We compare models with difference mechanisms of breaking the scale invariance: “hard breaking” (by relevant operators) and “soft breaking” (by marginal operators). We find that the thermalization time of the transverse traceless fluctuations of the stress-energy tensor is rather insensitive to the mechanisms of breaking the scale invariance over a large range of the scale-breaking parameter $\delta =\frac{1}{3}-c_s^2$. We comment on the relevance of the results to QCD quark-gluon plasma.

Figure 1

Parametrization of $\mathrm{\Theta }=\frac{\epsilon -3p}{\epsilon }$ with $\delta =\frac{1}{3}-c_s^2$ in the strongly coupled gauge theory plasma for QCD (the red dots), $\mathcal{N}=2^{*}$ (the solid green line), and cascading gauge theory (the solid blue line). The dashed red line represents the conformal violation parameter $\delta$ in QCD at $T=0.3\mathrm{GeV}$. The black dot is the $\frac{m}{T}\to 0$ limit of $\mathcal{N}=2^{*}$ thermodynamics. Vertical blue lines represent the phase transitions in cascading gauge theory plasma: the confinement/deconfinement (dashed) and the chiral symmetry breaking (dotted).

Figure 2

Minus imaginary part of the lowest quasinormal mode at zero spatial momentum of the transverse traceless fluctuations of the stress-energy tensor in $\mathcal{N}=2^{*}$ (the solid green line) and KS (the solid blue line) gauge theory plasma as a function of $\delta =\frac{1}{3}-c_s^2$. The black dot denotes the lowest quasinormal mode of the dimension $\mathrm{\Delta }=5$ operator of the effective five-dimensional CFT in the deep IR of $\mathcal{N}=2^{*}$ plasma; see (3.1). The dashed red line represents the conformal violation parameter $\delta$ in QCD at $T=0.3\mathrm{GeV}$. Vertical blue lines represent the phase transitions in cascading gauge theory plasma: the confinement/deconfinement (dashed) and the chiral symmetry breaking (dotted).

Figure 3

Momentum dependence of the lowest quasinormal mode of the transverse traceless fluctuations of the stress-energy tensor in cascading gauge theory plasma at the ultraviolet fixed point (solid lines), the deconfinement phase transition (dashed lines), and the chiral symmetry breaking phase transition (dotted lines). The green/red lines represent the real/minus imaginary parts of the frequencies. The data are normalized to zero momentum values of the frequencies; see (3.2).