Entropic destruction of heavy quarkonium in non-Abelian plasma from holography

Lattice QCD indicates a large amount of entropy associated with the heavy quark-antiquark pair immersed in the quark-gluon plasma. This entropy grows as a function of the interquark distance giving rise to an entropic force that can be very effective in dissociating the bound quarkonium states. In addition, the lattice data show a very sharp peak in the heavy quark-antiquark entropy at the deconfinement transition. Since the quark-gluon plasma around the deconfinement transition is strongly coupled, we employ the holographic correspondence to study the entropy associated with the heavy quark-antiquark pair in two theories: (i) $\mathcal{N}=4$ supersymmetric Yang-Mills and (ii) a confining Yang-Mills theory obtained by compactification on a Kaluza-Klein circle. In both cases we find the entropy growing with the interquark distance and evaluate the effect of the corresponding entropic forces. In the case (ii), we find a sharp peak in the entropy near the deconfinement transition, in agreement with the lattice QCD results. This peak in our holographic description arises because the heavy quark pair acts as an eyewitness to the black hole formation in the bulk—the process that describes the deconfinement transition. In terms of the boundary theory, this entropy likely emerges from the entanglement of a “long string” connecting the quark and antiquark with the rest of the system.

Figure 1

Left: Lattice QCD result for the entropy of the quark–antiquark pair at large separation in QCD plasma, as a function of $T/T_c$; from [13]. Right: Lattice QCD result for the entropy of the quark–antiquark pair as a function of the separation $r$ (denoted as $L$ in this paper) at temperature $T\sim 1.3T_c$; from [13]. The arrow on the right points the value of the entropy $T{S}_{\infty }$ at the large distance limit, which corresponds to the left figure.

Figure 2

The entropy of the quark-antiquark pair in the $\mathcal{N}=4$ SYM plasma, as a function of $LT$. For $LT>c\simeq 0.24$, the quark and the antiquark are screened and the entropy is constant ($S_{\text{str}}^{(2)}$). For smaller values of $LT$, the entropy grows approximately as $(LT{)}^3$ [see the expression (11) for $S_{\text{str}}^{(1)}$].

Figure 3

A schematic plot of the entropy of the quark-antiquark pair at large distance in the confining Yang-Mills theory as a function of $T/T_c$, as given by the holographic result (22). The entropy diverges at $T=T_c$. For low temperatures $T<T_c$ the entropy vanishes, while for high temperatures $T>T_c$ it has a finite value proportional to the temperature.

Figure 4

A sketch of the holographic dual of the quark-antiquark pair in the confining gauge theory. The left panel depicts a confining phase, and the right panel—the deconfined phase. The horizontal axis is the holographic direction $U$, and the vertical axis is our 3-dimensional space. The quark-antiquark pair is connected by a fundamental string hung down from the boundary of the geometry (located at the right edge of each figure). (Left) At low temperatures, and at a large inter-quark distance $L$, the string creeps at the bottom of the geometry. (Right) For a temperature higher than the critical temperature $T_c$, the string is divided into two parts. The dashed line is the would-be string at the horizon just at $T=T_c$ resulting in the peak of the entropy associated with the quark-antiquark pair.