Electric Field Quench in AdS/CFT†

K. Hashimoto,∗1,∗2 S. Kinoshita,∗3 K. Murata,∗4 and T. Oka∗5

In this paper, we analyze response of the stronglycoupled gauge theory against an electric field quench,by using the AdS/CFT correspondence. The system isN = 2 supersymmetric QCD with N = 4 super Yang-Mills as a gluon sector, and has a confining spectrumfor the meson sector (while the gluon sector is alwaysdeconfined). We turn on the electric field in a time-dependent manner, and find that the system developsto a deconfinement phase of mesons.

We study time-dependent behavior of various ob-servables such as electric current carried by the quarksand the quark condensate. We define the thermaliza-tion time scale and the deconfinement time in termsof the gravity dual side: the thermalization is with theHawking temperature, and the deconfinement is withthe strong redshift.

Among our findings, the most interesting is the factthat the deconfinement transition of the mesons oc-curs even with a small electric field once it is appliedtime-dependently. In the static electric field, there ex-ists a critical value of the electric field beyond whichthe electric current flows and the system is deconfined.In our time-dependent quench, if the quench is madesufficiently fast, even with a final electric field whichis smaller than the critical value, the system goes toa deconfinement phase — there appears a strong redshift region in the gravity dual.

In the dual gravity picture, this phenomena can beunderstood as the D-brane version of the weakly turbu-lent AdS instability. The wave packet on the D-braneis getting sharp as time increases and, eventually, col-lapses into the naked singularity. Accordingly, we alsofound a curious behavior of the deconfinement time —the time scale when a strong redshift region appearson the D7-brane. The deconfinement time takes onlydiscrete values.

Furthermore, the potential implication of thepresent study of nonequilibrium dynamics in QCDto strongly correlated electron system is suggestive.Then, it is tempting to speculate that the formation ofnaked singularity explained in the previous section isan indication of the “meson Mott transition”, i.e., theQCD version of the exciton Mott transition. We plot aschematic phase diagram obtained by this analogy inFig. 1 with three regions (i), (ii), and (iii).(i) Confinement phase with coherent oscilla-tion. When the field is weak, the system is always

† Condensed from the article in JHEP 1409 (2014) 126∗1 RIKEN Nishina Center∗2 Department of Physics, Osaka University∗3 Osaka City University Advanced Mathematical Institute∗4 Keio University∗5 Department of Applied Physics, University of Tokyo

QCD Schwinger limit (critical field)

Ef

pair creation

Ef

∆V

Ef

coherent oscillation ofvacuum polarization

“meson Mott transitio

n”

(iii) Deconfined nonequilibrium phase

(ii) Transient deconfined state

Ef

screening

(i) Confinement phase

Fig. 1. Schematic ”dynamical phase diagram” of states re-

alized in the present study by a static electric field Ef

following an initial ramp (parametrized by the time pa-

rameter ∆V ). See text for details.

in the confinement phase. However, when the rampspeed is fast (small ∆V ), the field induces a coherentoscillation of vacuum polarization due to meson exci-tation.(ii) Transient deconfined phase (“meson Motttransition”). This is the speculated “meson Motttransition” regime. When the meson amplitude be-comes large, the confinement force becomes relativelyweak due to screening. The quarks become liberatedand deconfinement takes place in the meson (quark)sector.(iii) Deconfined nonequilibrium phase aboveQCD Schwinger limit. When the electric fieldis stronger than the confining strength (= QCDSchwinger limit), the confinement phase becomes un-stable against direct pair creation of quark and anti-quarks.1). This state is a static nonequilibrium phasewith finite current.

In summary, by studying the dynamics of supersym-metric QCD in strong electric fields, we observed manyinteresting, and universal nonequilibrium physics. Ourfinding implies similarities between possible formationmechanism of quark gluon plasma in heavy ion col-lision experiments to laser induced phase transitionsin condensed matter, which helps us understand thephysics more deeply.

References1) K. Hashimoto and T. Oka, JHEP 1310, 116 (2013)

[arXiv:1307.7423].

Holographic entanglement and causal shadowin the time-dependent Janus black hole†

Y. Nakaguchi,∗1,∗2 N. Ogawa,∗3 and T. Ugajin∗4

The relation between entanglement and the blackhole interior has been attracting attention recently.For eternal AdS black holes, some interior informationis captured by the entanglement entropy of an intervalon the dual theory, i.e. a thermofield doubled CFT1).In some kinds of black holes, the interior appears

even more difficult to access since they have “causalshadow” regions inside. In this work, we considerone such black hole, called the three-dimensional time-dependent Janus black hole2),

ds2 = L2

[dy2 +

r20g̃(y)2 cosh2 r0t

(−dt2 + dθ2)

],

g̃(y) =

√2

1 +√

1− 2γ2 cosh 2y, (1)

where γ is a deformation parameter from the BTZblack hole. This is a solution of the Einstein-scalartheory and it corresponds to a pair of two entangled2D CFTs, whose coupling constants are different fromeach other.This geometry has a horizontally extended Penrose

diagram as shown in Fig. 1. The remarkable prop-erty of this geometry is the existence of a so-called“causal shadow region,” which is causally inaccessiblefrom both boundaries.

pastEH

futureEH

y

t

AH

−∞ +∞

+∞

−∞

Fig. 1. Penrose diagram of the 3D time-dependent Janus

black hole. The causal shadow is painted yellow. The

apparent horizons (green line) in the time slices τ =

const. are located inside the future event horizon.

We studied the time-evolution of the same entan-

† Condensed from the article arXiv:1412.8600 [hep-th].∗1 Institute for the Physics and Mathematics of the Universe,

University of Tokyo∗2 Department of Physics, University of Tokyo∗3 RIKEN Nishina Center∗4 Kavli Institute for Theoretical Physics, University of Cali-

fornia

glement entropy in this system in a holographic man-ner, by using the Ryu-Takayanagi formula. As in theBTZ black hole, there are two candidate extremal sur-faces in the bulk, whose area gives the entanglemententropy. One of the extremal surfaces, which we callthe connected surface, connects two asymptotic bound-aries and probes the black hole interior. The other ex-tremal surface, which we call the disconnected surface,localizes near each of the asymptotic boundaries.

In the Janus black hole, when the deformation fromthe BTZ black hole is not so large, we found a simi-lar behavior but with the critical time tc shorter thanthat of the BTZ black hole. Roughly speaking, this isbecause the deformation makes the wormhole regionlonger and results in a longer connected surface. Theresults for the time evolution of the entanglement en-tropy of each phase are plotted in Fig. 2.

In addition, we also found that with a sufficientlylarge deformation, the disconnected surface is alwaysdominant, and that the holographic entanglement en-tropy is already proportional to the size of the subsys-tem from the initial time. This means that the entan-glement entropy of this subsystem does not probe theblack hole interior.

Γ2� 0.3Adc �Numerical�Early approx. �t��Θ�Late approx. �Θ��t�O�Γ2�Ac

0 2 4 6 8 t8.0

8.5

9.0

9.5

10.0

10.5

11.0A�t,Θ �5�

Fig. 2. The time t dependence of the extremal surface area

A for a subsystem θ = 5, in the disconnected phase

(black dotted line, numerically obtained) and in the

connected phase (gray line).

References1) T. Hartman and J. Maldacena, JHEP 1305 (2013)

014, [arXiv:1303.1080].2) D. Bak, M. Gutperle, and S. Hirano, JHEP 0702

(2007) 068, [hep-th/0701108].3) D. Bak, M. Gutperle, and A. Karch, JHEP 0712

(2007) 034, [arXiv:0708.3691].

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