Holographic entropy and real-time dynamics of quarkonium dissociation in non-Abelian plasma

The peak of the heavy quark pair entropy at the deconfinement transition, observed in lattice QCD, suggests that the transition is effectively driven by the increase of the entropy of bound states. The growth of the entropy with the interquark distance leads to the emergent entropic force that induces dissociation of quarkonium states. Since the quark-gluon plasma around the transition point is a strongly coupled system, we use the gauge-gravity duality to study the entropy of heavy quarkonium and the real-time dynamics of its dissociation. In particular, we employ the improved holographic QCD model as a dual description of large $N_c$ Yang-Mills theory. Studying the dynamics of the fundamental string between the quarks placed on the boundary, we find that the entropy peaks at the transition point. We also study the real-time dynamics of the system by considering the holographic string falling in the black hole horizon where it equilibrates. In the vicinity of the deconfinement transition, the dissociation time is found to be less than a fermi, suggesting that the entropic destruction is the dominant dissociation mechanism in this temperature region.

Figure 1

The horizon of the large black hole branch in terms of the temperature, in units of critical temperature.

Figure 2

The entropy of the heavy quark-antiquark pair in the deconfined phase, as calculated in the IHQCD model (red curve) and in the lattice QCD (blue points). The lattice points were calculated in Ref. [2]. In the y axis, it is the entropy times the temperature in MeV, and the x axis is the temperature in units of $T_c$.

Figure 3

The string extending toward the horizon, for $L=8r_H$, in the case of the AdS-Schwarzschild black hole. We notice that the bulk part of the string is actually a straight line, independent on $x$.

Figure 4

The string motion from the boundary to the horizon in the improved holographic QCD background. This is the case of the large separation distance of the quark-antiquark pair. The black hole temperature is $T=T_c$.

Figure 5

The quarkonium dissociation time in terms of the temperature in units of $T_c$.