RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-6. Particle Physics

Meson turbulence at quark deconfinement from AdS/CFT†K. Hashimoto,∗1,∗2 S. Kinoshita,∗3 K. Murata,∗4 and T. Oka∗5
How the quarks are conﬁned at the vacuum of quantum chromodynamics (QCD) is one of the most fundamental questions in the standard model of particle
physics. We would like to ﬁnd a universal feature of
the deconﬁnement. To understand the nature of thequark conﬁnement, we need a proper observable which
exhibits a universal behavior irrespective of how webreak the conﬁnement. In this paper, we propose auniversal behavior of resonant mesons and name it meson turbulence.
Following our previous paper1) , we ﬁnd that a particular behavior of resonant mesons (excited states ofmesons) can be an indicator of the deconﬁnement. The
meson turbulence is a power-law scaling of the resonant meson condensations. For the the resonant meson level n (n = 0, 1, 2, · · ·), the condensation of themeson ⟨cn (x, t)⟩ with its mass ωn causes the n-th meson energy εn scaling as (ωn )α with a constant power
α. This coeﬃcient α will be unique for a given theory,and does not depend on how one breaks the conﬁnement. In particular, for the theory which we analyze inthis paper, that is N = 2 supersymmetric QCD with
N = 4 supersymmetric Yang-Mills as its gluon sector
at large Nc at strong coupling, the universal power-law
scaling parameter α is found to be⟨εn ⟩ ∝ (ωn )α ,α = −5 .

(1)

where εn is the energy of the n-th meson resonance.
Normally, for example at a ﬁnite temperature, the energy stored at the n-th level of the resonant meson
should be a thermal distribution, εn ∝ exp[−ωn /T ].
The thermal distribution is Maxwell-Boltzmann statistics, in which the higher (more massive) meson modes
are exponentially suppressed. However, we conjecturethat this standard exponential suppression will be replaced by a power-law near any kind of the deconﬁnement transitions. If we think of the meson resonantlevel n as a kind of internal momentum, then the energy ﬂow to higher n can be regarded as a so-called
weak turbulence. This is why we call the phenomenon
meson turbulence, and the level n can be indeed regarded as a momentum in holographic direction in theAdS/CFT correspondence.
The reason we came to the universal power behavior
is quite simple. We combined two well-known things,
†

∗1
∗2
∗3
∗4
∗5

• Mesons are excitations of an open QCD string.

Fig. 1. A schematic picture of the deconfinement phase ascondensation of QCD strings. Left: we add a meson (apair of a quark and an anti-quark connected by a QCDstring) to the system. Right: due to the backgroundcondensed QCD strings, the QCD string can be reconnected, and the quark can freely propagate away fromthe anti-quark.

• Deconﬁnement phase is described by a condensation of long strings.
Combining these two leads us to the conjecture that thedeconfinement of quarks is indicated by a condensationof higher meson resonances. More precisely, we claimthat the condensation should be turbulent: the higher
mode condensation is not suppressed exponentially but
behaves with a power-law.
We shall investigate various deconﬁning transitionsin this paper, to check the universality of our conjecture of the meson turbulence. First, we work with astatic case. A nonzero electric ﬁeld is a good example since a strong electric ﬁeld can make the quarkantiquark pair dissociate. Then we investigate timedependent setup. The virtue of the AdS/CFT correspondence is that time-dependent analysis is possible,
as opposed to lattice simulations of QCD. To demonstrate the universality of the meson turbulence, wework in two examples: (1) electric-ﬁeld quench, and(2) quark-mass quench. In all cases, we ﬁnd numerically the meson turbulence and the universal powerlaw with the power α = −5.

The universality we found in this paper strongly indicates that the meson turbulence is a universal phenomena which is independent of how one breaks theconﬁnement.
References
1) K. Hashimoto, S. Kinoshita, K. Murata and T. Oka,
arXiv:1408.6293 [hep-th].

Condensed from the article in arXiv:1412.4964
RIKEN Nishina Center
Department of Physics, Osaka University
Osaka City University Advanced Mathematical InstituteKeio University
Department of Applied Physics, University of Tokyo- 150 -完全版2014_本文.indd 150

15/10/16 17:49