Ⅱ-6. Particle Physics

RIKEN Accel. Prog. Rep. 48 (2015)

Entropic destruction of heavy quarkonium in non-Abelian plasma
from the holographic correspondence†
K. Hashimoto∗1,∗2 and D. E. Kharzeev∗3
The studies of heavy quarkonium at finite temperature are expected to advance the understanding ofQCD plasma and to clarify the nature of the deconfinement transition. It was originally proposed1) touse the quarkonium suppression in heavy ion collisions
as a way to detect the Debye screening in the quarkgluon plasma. The subsequent experimental studiesof quarkonium production at different energies however revealed a puzzle – the charmonium suppression
observed at RHIC (lower energy density) appearedstronger than at LHC (larger energy density). This isin contrast to both the Debye screening scenario1) andthe thermal activation through the impact of gluons.
One possible solution to this puzzle is the recombination of the produced charm quarks into charmonia.
However, recently it was argued2) that an anomalously strong suppression of charmonium near the deconfinement transition can be a consequence of thenature of deconfinement. The argument put forward
in Ref.2 was based on the lattice QCD results indicating a large amount of entropy associated with theheavy quark-antiquark pair placed in the quark-gluon
plasma. This entropy S was found on the lattice togrow as a function of the distance L between the quark
and antiquark. The proposal of2) is that this entropy
should thus lead to the emergent entropic force
F =T

∂S,
∂L

(1)

where T is the temperature of the plasma. It has beenfound that the balance of the attractive force from theinternal interaction and the repulsive entropic force
indicates a strong suppression of charmonium statesnear the deconfinement transition. The leading role ofthe entropic force in the deconfinement transition itself
has been conjectured, as well as a possible link of theobserved peak in the entropy near the deconfinementtransition to the “long string” condensation.
In this paper, we investigate the microscopic originof the entropy associated with the heavy quark pair in
non-Abelian plasma using the holographic correspondence (the AdS/CFT correspondence). We conclude
that the narrow and strong peak in the entropy associated with the heavy quark pair near the transition temperature is indeed related to the nature of deconfinement, and in holographic description originates†∗1∗2∗3Condensed from the article in Phys. Rev. D90, 125012(2014)RIKEN Nishina Center
Department of Physics, Osaka University
Department of Physics and Astronomy, Stony Brook University

from the entropy of a long fundamental string at thebottom of the confining geometry which would be absorbed into a black hole horizon after a deconfinementtransition. It is absent in the conformal N = 4 supersymmetric Yang-Mills theory, but emerges in a confining Yang-Mills theory obtained by compactification of
the fifth dimension. On the boundary, this entropy has
to be attributed to long-range, delocalized excitations
entangled with the heavy quark pair that can indeed
be described as the “long string”.
The origin of this peak in the holographic description is intriguing – it arises because the heavy quark
pair acts as an eyewitness of the black hole formationin the confining (at low temperatures) bulk geometry.
This process of black hole formation is the dual holographic representation of the deconfinement transitionon the boundary. From this viewpoint, the entropy
associated with the quark-antiquark pair is the rightquantity to detect the temperature at which the deconfinement occurs.
We also study the entropic force in holographic setup of strongly coupled gauge theories. It turns outthat the entropic force associated with the distributionof the quarks is at a sub-leading order in the strong
coupling expansion in terms of the ’tHooft coupling
constant, while the entropic force of the QCD stringis comparable to the quark-antiquark force. Howevera reasonable evaluation of the sub-leading term showsthat the Einstein entropic force increases such that thecritical distance of the quark pair to be destructed entropically is shortened.
Our proposal of using the entropy associated withthe heavy quark-antiquark pair to detect the deconfinement transition is somewhat similar to the idea ofusing the entanglement entropy as an order parameterof deconfinement. The difference is that the order parameter discussed in is the von Neumann entanglement
entropy of a spatial region with a boundary, while weconsider the Gibbs entropy. In terms of the boundary
theory, the entropy of the quark-antiquark pair likely
emerges from the entanglement of a “long string” connecting the quark and antiquark with the rest of thesystem. It would be interesting to clarify this issue
further as it may improve our understanding of both
deconfinement and confinement.
References
1) T. Matsui and H. Satz, Phys. Lett. B 178, 416 (1986).
2) D. E. Kharzeev, Phys. Rev. D 90, 074007 (2014)[arXiv:1409.2496 [hep-ph]].
3) K. Hashimoto and T. Oka, JHEP 1310, 116 (2013)[arXiv:1307.7423].

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