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Meson Turbulence at Quark Deconfinement from Ads/CFT†

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Meson Turbulence at Quark Deconfinement from Ads/CFT† RIKEN Accel. Prog. Rep. 48 (2015) Ⅱ-6. Particle Physics Ⅱ-6. Particle Physics RIKEN Accel. Prog. Rep. 48 (2015) Meson turbulence at quark deconfinement from AdS/CFT† Electromagnetic instability in holographic QCD† 1, 2 3 4 5 1, 3 2 3 K. Hashimoto,∗ ∗ S. Kinoshita,∗ K. Murata,∗ and T. Oka∗ K. Hashimoto,∗ ∗ T. Oka,∗ and A. Sonoda∗ How the quarks are confined at the vacuum of quan- Schwinger effect2) is one of the most interesting phe- part of the Lagrangian. We found that the creation tum chromodynamics (QCD) is one of the most fun- nomena in particle physics. This is a phenomenon that rate diverges at a zero temperature in the massless damental questions in the standard model of particle a pair creation of charged particles occur under an ex- quark limit while it becomes finite when we introduce physics. We would like to find a universal feature of ternal field such as an electromagnetic field. Schwinger a nonzero temperature. The divergence of the creation the deconfinement. To understand the nature of the obtained the creation rate of an electron positron pair rate is influenced not only by a constant electric field quark confinement, we need a proper observable which by evaluating the imaginary part of Euler-Heisenberg but also by a constant magnetic field. The results in exhibits a universal behavior irrespective of how we Lagrangian1), which is an effective Lagrangian for a SQCD showed similarities with the creation rate of break the confinement. In this paper, we propose a constant electric field. This rate Γ is derived as the electron positron pair in = 2 supersymmetric universal behavior of resonant mesons and name it me- Γ exp πm2/eE to leading order and has a form QED(SQED) in constant electromagneticN field. Fig. 1. A schematic picture of the deconfinement phase as e son turbulence. with∼ a negative− power in the gauge coupling e. So the In this paper, we study the quark antiquark pair condensation of QCD strings. Left: we add a meson (a Scwinger effect is a non-perturbative effect. Here, m creation in non-supersymmetric QCD at large N at Following our previous paper1), we find that a par- pair of a quark and an anti-quark connected by a QCD e c is the electron mass and E is an electric field. A critical strong coupling, and the imaginary part of D8-brane ticular behavior of resonant mesons (excited states of string) to the system. Right: due to the background electric field necessary energy for the electron positron action in a constant electromagnetic field. The holo- mesons) can be an indicator of the deconfinement. The condensed QCD strings, the QCD string can be recon- pair creation is E m2c3/e¯h, and the strength is graphic models are the Sakai-Sugimoto model6) and meson turbulence is a power-law scaling of the reso- nected, and the quark can freely propagate away from cr e about 1018 [V/m]. So,∼ it is a phenomenon which shows its deformed version. Our findings in this paper are as nant meson condensations. For the the resonant me- the anti-quark. up only under strong electromagnetic fields. follows: son level n (n =0, 1, 2, ), the condensation of the ··· Recently, we have seen advance in research on a meson cn(x, t) with its mass ωn causes the n-th me- We derive the Euler-Heisenberg Lagrangian for ⟨ ⟩ α strong electromagnetic field in both theoretical and ex- • son energy εn scaling as (ωn) with a constant power Deconfinement phase is described by a condensa- confining gauge theories: the Sakai-Sugimoto • perimental aspects of hadron physics. At the heavy ion α. This coefficient α will be unique for a given theory, tion of long strings. model and the deformed Sakai-Sugimoto model. collision in RHIC and LHC, it is expected that a strong and does not depend on how one breaks the confine- We obtain the creation rate of the quark antiquark Combining these two leads us to the conjecture that the magnetic field is generated by a collision of charged ment. In particular, for the theory which we analyze in pair under the electromagnetic field, by evaluating deconfinement of quarks is indicated by a condensation particles accelerated at about the speed of light. this paper, that is = 2 supersymmetric QCD with the imaginary part of the D-brane actions. N of higher meson resonances. More precisely, we claim Within the AdS/CFT framework, the quark pair = 4 supersymmetric Yang-Mills as its gluon sector The imaginary part is found to increase with the N that the condensation should be turbulent: the higher creation rate in the strongly coupled = 4 super- • at large Nc at strong coupling, the universal power-law magnetic field parallel to the electric field, while mode condensation is not suppressed exponentially but symmetric Yang-Mills theory was obtainedN in3). On scaling parameter α is found to be it decreases with the magnetic field perpendicular behaves with a power-law. the other hand, two of the present authors obtained to the electric field. So the vacuum instability ε (ω )α,α= 5 . (1) the vacuum decay rate, which can be identified as the n n We shall investigate various deconfining transitions strongly depends on the direction of the applied ⟨ ⟩∝ − creation rate of quark-antiquark pairs, in = 2 super- in this paper, to check the universality of our conjec- magnetic field relative to the electric field. where εn is the energy of the n-th meson resonance. symmetric QCD(SQCD) by using a differentN method4) ture of the meson turbulence. First, we work with a We obtain a critical value of the electric field, i.e., Normally, for example at a finite temperature, the en- in AdS/CFT correspondence: the imaginary part of static case. A nonzero electric field is a good exam- • the Schwinger limit, by using the condition that ergy stored at the n-th level of the resonant meson the probe D-brane action. D3-D7 brane system corre- ple since a strong electric field can make the quark- the D-brane action has the imaginary part. In should be a thermal distribution, εn exp[ ωn/T ]. sponds to = 4 supersymmetric SU(N ) Yang-Mills ∝ − antiquark pair dissociate. Then we investigate time- c the case of the Sakai-Sugimoto model, the critical The thermal distribution is Maxwell-Boltzmann statis- theory includingN an = 2 hypermultiplet in the fun- tics, in which the higher (more massive) meson modes dependent setup. The virtue of the AdS/CFT corre- N electric field corresponds to a QCD string tension damental representation of the SU(Nc) gauge group. are exponentially suppressed. However, we conjecture spondence is that time-dependent analysis is possible, between a quark and an antiquark. as opposed to lattice simulations of QCD. To demon- They obtained the creation rate of the quark antiquark that this standard exponential suppression will be re- in the = 2 SQCD under a constant electric field As for the first part among above, a result with only placed by a power-law near any kind of the deconfine- strate the universality of the meson turbulence, we N work in two examples: (1) electric-field quench, and by evaluating the imaginary part of the D7-brane ac- an electric field was reported in Ref. 7). We analyze ment transitions. If we think of the meson resonant tion. Then, the present authors evaluated the imag- generic electric and magnetic fields in this paper. level n as a kind of internal momentum, then the en- (2) quark-mass quench. In all cases, we find numer- ically the meson turbulence and the universal power inary part of the D7-brane action including not only ergy flow to higher n can be regarded as a so-called References law with the power α = 5. a constant electric field but also a constant magnetic weak turbulence. This is why we call the phenomenon − field and obtained the creation rate of the quarks and 1) J. S. Schwinger, Phys. Rev. 82 (1951) 664. meson turbulence, and the level n can be indeed re- The universality we found in this paper strongly in- antiquarks in the = 2 SQCD5). 2) W. Heisenberg and H. Euler, Z. Phys. 98 (1936) 714 garded as a momentum in holographic direction in the dicates that the meson turbulence is a universal phe- We summarizeN the properties of the creation rate [physics/0605038]. AdS/CFT correspondence. nomena which is independent of how one breaks the in both electric and magnetic fields obtained in5) for 3) G. W. Semenoff and K. Zarembo, Phys. Rev. Lett. 107 (2011) 171601 [arXiv:1109.2920 [hep-th]]. The reason we came to the universal power behavior confinement. = 2 SQCD as follows. We derived the Euler- N 4) K. Hashimoto and T. Oka, JHEP 1310, 116 (2013) is quite simple. We combined two well-known things, Heisenberg Lagrangian for a constant electromagnetic References [arXiv:1307.7423]. field in = 2 SQCD at large Nc and at strong cou- 5) K. Hashimoto, T. Oka and A. Sonoda, JHEP 1406 Mesons are excitations of an open QCD string. 1) K. Hashimoto, S. Kinoshita, K. Murata and T. Oka, pling.N Then, we obtained the creation rate of the • arXiv:1408.6293 [hep-th]. (2014) 085 [arXiv:1403.6336 [hep-th]]. † Condensed from the article in arXiv:1412.4964 quarks and antiquarks by evaluating the imaginary 6) T. Sakai and S. Sugimoto, Prog. Theor. Phys. 113 1 ∗ RIKEN Nishina Center 2 (2005) 843 [hep-th/0412141]. ∗ Department of Physics, Osaka University † Condensed from the article in arXiv:1412.4254 3 1 7) K.
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