ゲージ・重力対応による非平衡相転移と対称性の自発的破れ
松本 匡貴 (中央大学)
共同研究者：中村真、今泉拓也

Outline• Introduction• Non-equilibrium steady state : conducting system• Non-equilibrium phase transition• Critical behavior• SummaryD3-D7 at finite temperature
AdS-BH : ds =24 2
41 (1 z 4 /zH) 2 1 + z 4 /zHdz 22d~x + 24 dt +
z 2 1 + z 4 /zHz2z

DBI Action : SD7 = TD7<latexit sha1_base64="Bn1O1wz/qh076Ypowcvu2UTWnHE=">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</latexit>
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multiplet

Z

8

d ⇠

p

Dualitydet(gab + (2⇡↵0 )Fab )AdS Black hole spacetime
D7-braneMesonm<latexit sha1_base64="+Scr/O1DZ7pTN/mhxqvit+4Paas=">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</latexit><latexit
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Gluon

Heat bath T =<latexit sha1_base64="VW1kK/FpalBAzjyAFyvX+28m8J4=">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</latexit>
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Chiral condensate : hq q̄i =<latexit sha1_base64="DMva3WEBcNNnQJTAYw9PMBy1CzY=">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</latexit>
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sha1_base64="QX0BKJn5xPX72dIkUgt8lfVgD1k=">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</latexit>zH : horizon⇡zHm

Quark mass :AdS-BH1
2✓2 + m3
3

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sha1_base64="+7a0sh6M4HjPZSSE3mfcmuzGVEM=">AAACZnichVG7SgNBFD1ZXzG+ouIDbIISsQp3bRSrEBtLY4wKKmF3ncTBfbG7CWjwBwRbU1gpiIj4FVr4AxY21oqlgo2FN5uAqKh3mJkzZ+65c2ZGd03pB0T3EaWlta29I9oZ6+ru6e2L9w+s+E7ZM0TecEzHW9M1X5jSFvlABqZYcz2hWbopVvWd+fr+akV4vnTs5WDXFZuWVrJlURpawFRur7BQiE9QisJI/ARqE0ykh7MP8ipzs+jEz7GBLTgwUIYFARsBYxMafG7rUEFwmdtElTmPkQz3BfYRY22ZswRnaMzu8Fji1XqTtXldr+mHaoNPMbl7rEwgSXd0QS90S5f0RO+/1qqGNepednnWG1rhFvoORnNv/6osngNsf6r+9BygiNnQq2TvbsjUb2E09JW92ktubilZnaRTemb/J3RP13wDu/JqnGXF0jFi/AHq9+f+CVamUyql1Cz/RAaNiGIM45ji955BGgtYRJ7PLeEQR6hFHpVeZUgZaaQqkaZmEF9CSXwANUGOUg==</latexit>

D7-brane embedding function✓(z) = mz + ✓2 z 3 + · · ·<latexit sha1_base64="6QiR+/BRvqzO/dki8f6KnAcBSc0=">AAACiXichVHLLgRBFD3aa4zXYCOx6RiESCa3WRCJZMLG0muQGCbdrYaOfqW7ZhIz8QN+wMKKRERsbNna+AELnyCWJDYW7vR0Ighup6vOPXXPrVNVhm9boSR6bFAam5pbWhNtyfaOzq7uVE/vWuiVAlPkTM/2gg1DD4VtuSInLWmLDT8QumPYYt3Yn6+tr5dFEFqeuyoPfLHl6LuuVbRMXTJVSA3l5Z6Q+mhlbNZRK+p4PS1MqJXtSXVczZs7ngwLqTRlKAr1J9BikEYci17qAnnswIOJEhwIuJCMbegI+duEBoLP3BaqzAWMrGhd4BBJ1pa4SnCFzuw+j7ucbcasy3mtZxipTd7F5j9gpYpheqBLeqF7uqInev+1VzXqUfNywLNR1wq/0H3Uv/L2r8rhWWLvU/WnZ4kipiOvFnv3I6Z2CrOuL1eOX1ZmloerI3RGz+z/lB7pjk/gll/N8yWxfIIkP4D2/bp/grWJjEYZbYnS2bn4KRIYwCBG+b6nkMUCFpHjfY9wjRvcKu2KpkwrM/VSpSHW9OFLKPMfGCmV6g==</latexit>
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sha1_base64="8owk6OVYfTUCg4/ZbfxomcJlYP0=">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</latexit>

Conducting system in D3-D7
Gauge fieldAx (t, z) =Et + ax (z),Ay (x) = Bx

: external electric field: external magnetic field<latexit sha1_base64="49jxmAgrbKcqxwoghSA+kc3CrJs=">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</latexit>
sha1_base64="EHZUvxigoiymHJN0ny1ECcXZVRU=">AAACtnicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQtoqznGV1fUapToVGna6roqlChoJ4IFqjR1FGJiuEDSlbUaFZq2ThXxAsoGegZgoIDJMIQylBmgICBfYBdDDEMKQz5DMkMpQy5DKkMeQwmQncOQyFAMhNEMhgwGDAVAsViGaqBYEZCVCZZPZahl4ALqLQWqSgWqSASKZgPJdCAvGiqaB+SDzCwG604G2pIDxEVAnQoMqgZXDVYafDY4YbDa4KXBH5xmVYPNALmlEkgnQfSmFsTzd0kEfyeoKxdIlzBkIHThdXMJQxqDBditmUC3F4BFQL5Ihugvq5r+OdgqSLVazWCRwWug+xca3DQ4DPRBXtmX5KWBqUGz8bgnCejvRCA/FWhmLTCaDNEjBZMRZqRnaKBnGGii7OABjTAOBmkGJQYNYKyYMzgweDAEMIQCbZnIsJ3hAMNBJgumOKZUpnSIUiZGqB5hBhTAVAAA24GgQg==</latexit>

2J 2 = (2⇡↵0 )2 |gtt |gxx
cos6 ✓(z⇤ )Current density :<latexit sha1_base64="KZtkWbWp35WFQSYbacdTrbsUceM=">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</latexit>
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4effective horizon : z⇤ =<latexit sha1_base64="faSATmm3nE7IgfvAbXYcehyp/lM=">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</latexit>
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sha1_base64="7xc1GL/L04kgpgLppuS4jXxMdAo=">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</latexit>⇣

2F (E, B)p(2F (E, B)

1)2

1

⌘

4
1 zH

Solve EOM for D7-brane
embedding function numericallyThe quark mass is obtained fromthe asymptotic form.

J · E 6= 0
<latexit sha1_base64="P0wmkTIdfjT02s5uiO7LBJJjFKE=">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</latexit>
sha1_base64="/37RbdmkOKJOTlqXSDcsEIDFyQ0=">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</latexit>In massless case, are there possible solutions of D7-brane configuration?
・ trivial one : ✓(z) = 0 (always solution)<latexit sha1_base64="eeEUuBCf7oujx8DiHXKO9Pk0rvo=">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</latexit>
sha1_base64="m4mboTvsjXojAljHmmq8m09OTL8=">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</latexit>
sha1_base64="kLVWR/c84PoLgZgcDXFUuyrS7s0=">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</latexit>
sha1_base64="fA8eJnL45oqFx+uGDiOuMxLIiPg=">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</latexit>SO(2) rotational symmetry is preserved.

Flat branch・ non-trivial one : ✓(z) 6= 0 (in electric field and magnetic field)<latexit sha1_base64="yQPHI0HK3eyDp//nXcocJHYDVa0=">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</latexit>
sha1_base64="oK9S/Xmzn6M/oYgnqYEoMFzClEs=">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</latexit>
sha1_base64="ctRLThQHG5tEc/SCqbppHcPwGBU=">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</latexit>
sha1_base64="Vta2TQERPPtysVwi9PJPc/H7s2g=">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</latexit>SO(2) rotational symmetry is broken.

1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
00

0 924

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Bending BranchbranchFlat BranchFlatbranch<latexit sha1_base64="GE0RJd5Xcj4F5bz46o08cGAI6pA=">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</latexit>
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22<latexit sha1_base64="l3/D2Jj3F9evSvnAw/ju1dF77C4=">AAACZHichVG7SgNBFD1Z3zFqVARBkGCIWIW7aRQrwcbSqFEhhrC7TnRwX+xuAhr8AW0VCysFEfEzbPwBC39AEEsFGwvvbhZEg3qHmTlz5p47Z2Z015R+QPSYUDo6u7p7evuS/amBwaH08Mi679Q9Q5QMx3S8TV3zhSltUQpkYIpN1xOapZtiQ99bDPc3GsLzpWOvBfuuqFjaji1r0tACpoqFajpLeYoi0w7UGGQRx7KTvsYWtuHAQB0WBGwEjE1o8LmVoYLgMldBkzmPkYz2BQ6RZG2dswRnaMzu8bjDq3LM2rwOa/qR2uBTTO4eKzPI0QPd0Cvd0y0908evtZpRjdDLPs96Syvc6tDR+Or7vyqL5wC7X6o/PQeoYS7yKtm7GzHhLYyWvnFw9ro

33

44

66

55

r cos ✓

dual

SO(2)

U(1)χ

J-E characteristics and transitions
3.0
3.0<latexit sha1_base64="uFmfNh7PAW8+mbz59tsOSe0MYEo=">AAACZnichVHLSsNAFD2Nr1ofrYoouCkWxVW5qUKtK8GNS9vaVlCRJI41NC+StFCLPyC41YUrBRHxM9z4Ay78A8WlghsX3qZBEVHvMJkzZ+65cyZXdQzd84keIlJXd09vX7Q/NjA4NBxPjIyWPbvuaqKk2YbtbqiKJwzdEiVf9w2x4bhCMVVDVNTaSvu80hCup9vWut90xLapVC19T9cUn6nifJp2EilKUxDJn0AOQQphrNmJK2xhFzY01GFCwILP2IACj8cmZBAc5rbRYs5lpAfnAoeIsbbOWYIzFGZr/K3ybjNkLd63a3qBWuNbDJ4uK5OYoXu6phe6oxt6ovdfa7WCGm0vTV7VjlY4O/GjyeLbvyqTVx/7X6o/PfvYw2LgVWfvTsC0X6F19I2D05fiUmGmNUsX9Mz+z+mBbvkFVuNVu8yLwhliQQNyQSQ7ILsQgpz82YByJi1TWs5nUsurYSuimMI05vh/Z7GMVayhxPdWcYwTnEYepWFpXJropEqRUDOGbyElPwCy1Yq5</latexit>
sha1_base64="O85ZI/b39fTKhMGFo+nkGrtWyoo=">AAACZnichVHLSsNAFD2N76ptVUTBTbEorspNXSiuCm5c2tY+oIokcVpD0yQkaUGLPyC4tQtXCiLiZ7jxB1z0DxSXFdy48DYNiIp6h5k5c+aeO2dmVNvQXY+oE5IGBoeGR0bHwuMTk5FobGq64FoNRxN5zTIsp6QqrjB0U+Q93TNEyXaEUlcNUVRrm739YlM4rm6ZO96RLfbqStXUK7qmeEzlVpO0H0tQkvyI/wRyABIIYtuK3WAXB7CgoYE6BEx4jA0ocLmVIYNgM7eHFnMOI93fFzhBmLUNzhKcoTBb47HKq3LAmrzu1XR9tcanGNwdVsaxRI90S116oDt6pvdfa7X8Gj0vRzyrfa2w96On87m3f1V1nj0cfqr+9OyhgnXfq87ebZ/p3ULr65vH7W5uI7vUWqYremH/l9She76B2XzVrjMie4Ewf4D8/bl/gkIqKVNSzqQS6a3gK0axgEWs8HuvIY0tbCPP51ZxhnO0Q09SRJqV5vqpUijQzOBLSPEPdN+KKQ==</latexit>

B=14

2.5
2.5

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sha1_base64="iMC1P6ElntK7EtzSnQIu8Ol2md4=">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</latexit>

2.0

Bending branch

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sha1_base64="ZrYW9NjcF5tgbN5WMkS5lbPqklo=">AAACZnichVFNSwJBGH7cvsxKrYiCLpIYneRdL0UnoYvH1MygRHa30ZbW3WV3FUz6A0HXPHQqiIh+Rpf+QIf+QdGxoEuHXteFKKneYWaeeeZ93nlmRrUN3fWIHkPS0PDI6Fh4PDIxORWNxadntl2r6WiipFmG5eyoiisM3RQlT/cMsWM7Qmmohiirhxu9/XJLOK5umVte2xaVhlI39ZquKR5TxUyaqvEkpcmPxCCQA5BEEJtW/Bp72IcFDU00IGDCY2xAgcttFzIINnMVdJhzGOn+vsAxIqxtcpbgDIXZQx7rvNoNWJPXvZqur9b4FIO7w8oEUvRAN/RK93RLz/Txa62OX6Pnpc2z2tcKuxo7WSi+/6tq8Ozh4Ev1p2cPNaz5XnX2bvtM7xZaX9866r4W1wupzjJd0gv7v6BHuuMbmK037SovCueI8AfIP597EGxn0jKl5Xwmmc0FXxHGIpawwu+9iixy2ESJz63jFGfohp6kqDQnzfdTpVCgmcW3kBKfct2KKA==</latexit><latexit sha1_base64="am7Jc6YsOnW5B8m/3T2ALoclLlI=">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</latexit><latexit
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sha1_base64="L1bfx59kp2KIfvTwzhMJdbe2Kvo=">AAACcXichVHLSgMxFD0d3/VVdaO4KS2KIJQ7bhRXopsutbUq1Acz07QGp5lhZlrQ4g/4AwquLIiIn+HGH3DhJ4jLCm5ceDsdEBX1hiQnJ/fcnCSma0s/IHqKaV3dPb19/QPxwaHhkdHE2PiW79Q8SxQsx3a8HdPwhS2VKAQysMWO6wmjatpi2zxaa+9v14XnS0dtBseu2KsaFSXL0jICpvZXhSpJVUmanqGsw4NEmjIURvIn0COQRhTrTuIGuyjBgYUaqhBQCBjbMOBzK0IHwWVuDw3mPEYy3Bc4RZy1Nc4SnGEwe8RjhVfFiFW8btf0Q7XFp9jcPVYmMUOPdEsteqA7eqb3X2s1whptL8c8mx2tcA9Gzybzb/+qqjwHOPxU/ek5QBlLoVfJ3t2Qad/C6ujrJ+et/HJupjFLTXph/1f0RPd8A1V/ta43RO4Scf4A/ftz/wRbCxmdMvrGQnolG31FP6aRwhy/9yJWkMU6CnyuhwtcoRlraVNaUkt1UrVYpJnAl9DmPwCaKI9L</latexit>

1.5
1.5

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sha1_base64="baAoZ5FmzYJu0RC9Oc3zk9+s+jI=">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</latexit>

1.0
1.0

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sha1_base64="bVhutuWGzC8wjDmG6ulfDazCK/g=">AAACZnichVHLSsNAFD2Nr1pfVREFN8VScVVu3CiuCm667MO2gpaSxLEG0yQkaaEWf0BwaxeuFETEz3DjD7joHyguK7hx4W0aEC3qHWbmzJl77pyZUW1Ddz2iTkgaGh4ZHQuPRyYmp6ZnorNzRdeqO5ooaJZhObuq4gpDN0XB0z1D7NqOUGqqIUrq8XZvv9QQjqtb5o7XtEW5plRN/VDXFI+pvJykSjROSfIjNgjkAMQRRMaK3mIfB7CgoY4aBEx4jA0ocLntQQbBZq6MFnMOI93fFzhFhLV1zhKcoTB7zGOVV3sBa/K6V9P11RqfYnB3WBlDgp7ojrr0SPf0Qh+/1mr5NXpemjyrfa2wKzNnS/n3f1U1nj0cfan+9OzhEJu+V5292z7Tu4XW1zdO2t38Vi7RWqVremX/V9ShB76B2XjTbrIid4kIf4D887kHQXE9KVNSzq7HU+ngK8JYxgrW+L03kEIaGRT43CrOcYF26FmalhakxX6qFAo08/gWUuwTcNuKJw==</latexit>

Flat branch

0.5
0.5

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0.06
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J
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・We choose the current density as a control parameter.
・There is a multi-valued region at given J.
・Which solution is the most stable?
We assume that the most stable solution has the lowest“thermodynamic potential”.

Thermodynamic potential
F̃D7 = lim"!0<latexit sha1_base64="9KehGAoHweXk7aiTN8fck8G6P2k=">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</latexit>
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 Z z⇤"

dz H̃D7z⇤ : effective horizon

Lcount (")" : cutoff near boundary<latexit sha1_base64="YjxdCTEULRe6MsgVegnC9RPLvXY=">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</latexit>
sha1_base64="AduIqYkWFB6k/c2FWVr45U7bkRM=">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</latexit>@LD7
0 @LD7+ Ax
Hamiltonian density : H̃D7 = Ȧx
@A0x
@ Ȧx
s
p
J2
= gxx |gtt |gzz
gxx E 2LD7

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1
Counterterm : Lcount (") =4"4<latexit sha1_base64="YYMvZjg6thK3ZWuOXdbfnPdi+iM=">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</latexit>
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m2
5 4
+ m
2"2
12
massless

2 cos6 ✓|gtt |gxx
2|gtt |gxx|gtt |B 2

E2 + B2log ⇤"
2
Dimension [1/ε]In our study, we have chosen ⇤ as one of the possible choices so that
@ 2 LD7 /@E 2 = 0 or @ 2 LD7 /@B 2 = 0 for vacuum (T = 0, E = 0, B = 0) .
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zero polarizability

zero susceptibility

30
3.0

-12.0
12.0

Bending Branch
BendingbranchFlat
BranchFlat branch

-12.5
12.5

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2.5<latexit sha1_base64="GE0RJd5Xcj4F5bz46o08cGAI6pA=">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</latexit>
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20
2.0

-13.0
13.0

E

F̃D7

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13.5

15
1.5

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10
1.0

-14.0
14.0

-14.5
14.5
0.0
0.0
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05
0.5

0.1
0.1
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0.2
0.2

0.3
0.3

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0.4
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0.5
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0.0
00
00
0.0

0.6
0.6
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J

01
0.1

02
0.2

04
0.4

05
0.5

06
0.6

J

<latexit sha1_base64="30JxR1ESk5o6x+SKvF/rVkloB7k=">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</latexit><latexit
sha1_base64="8wwWStxtZTYkZqR6i+7WGtzvRGA=">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</latexit>

-15 0
15.0

03
0.3

6.06
5.05

-15 5
15.5

-16 0
16.0

E

F̃D7

4.04

B = 16

3.03
2.02

-16 5
16.5

1.01
17.0
-17 0
00

0.0

01
0.1

02
0.2

03
0.3

04
0.4

05
0.5

0.000 0
0.0

06
0.6

17.0

8.0

-18
18.0

6.06

-19
19.0

4.04

0.0

03
0.3

04
0.4

05
0.5

06
0.6

8

-20
20.0

-21
21.0
00

02
0.2

J

-17

E

F̃D7

J

01
0.1

B = 18

2.02

01
0.1

02
0.2

03
0.3

J

04
0.4

05
0.5

06
0.6

0.000 0
0.0

01
0.1

02
0.2

03
0.3

J

04
0.4

05
0.5

06
0.6

Order parameter : chiral condensate
We want a parameter which characterizes this phase transition.
Chiral condensate

Chiral condensate roughly corresponds to the non-flatness of the D7brane configuration.
D7-brane embedding function :Chiral condensate :3hq̄qi =✓(z) = mz + ✓2 z + · · ·<latexit sha1_base64="TKVeYjVgKJX3dg9PE3yG08PqawA=">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</latexit>
sha1_base64="uEbes2As92nSCkoNkLQwNaQH7YQ=">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</latexit><latexit sha1_base64="lCzrzyauGeMp/tAyDur+lSdLUZA=">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</latexit>
sha1_base64="eGGBkV2RVktHTGQ2OeIa7b1hBk4=">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</latexit>

12✓2 + m3
3

massless

1.4

Bending Branch
Flat Branch

1.2
1.0
0.8
0.6

hq̄qi =
6 0

0.4

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sha1_base64="Pu+7frilllHfN1m3Ife/aczrnPA=">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</latexit>

0.2
0.0

0

1

2

3

4

5

hq̄qi = 0<latexit sha1_base64="39r5Kt15KgKdbL/XYt9IL3N6op8=">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</latexit>
sha1_base64="H/6D2GtQ+Vm1XqhR0BK2yNYkSyM=">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</latexit>

6

35
35
30
30

35
35

(a)

B=18

25
25

hq̄qi

hq̄qi

20
20

20
20

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sha1_base64="GBZCV6wQkGd8jB4o48qPyf2rqAM=">AAACi3ichVE9S8NQFD3G789WXQRBikVxKjdV0IpgQQRHW60tqEgSX2swTUKSFmrp6CKu6uCk4CD+AXF1cXJz8CeIo4KLg7dJUUTUG/Leuefdc995XNU2dNcjemySmlta29o7Oru6e3r7QuH+gTXXKjmayGiWYTk5VXGFoZsi4+meIXK2I5SiaoisurtQP8+WhePqlrnqVWyxWVQKpp7XNcVjKh2nrXCUYuRH5CeQGyA6f3+det4fuV62wjfYwDYsaCihCAETHmMDClz+1iGDYDO3iSpzDiPdPxeooYu1Ja4SXKEwu8trgbP1BmtyXu/p+mqNbzH4d1gZwRg90CW90B1d0RO9/9qr6veoe6nwrgZaYW+FDoZW3v5VFXn3sPOl+tOzhzxmfK86e7d9pv4KLdCX905eVmbTY9VxOqdn9n9Gj3TLLzDLr9pFSqRP//Cj8rsVzgX3rPljSvgRCcD0VAMk5M8xrcVjMsXkFEWTSwiiA8MYxQRPZRpJLGEZGb4lj0Mc4VjqlSalWWkuKJWaGppBfAtp8QOKW5aS</latexit>J

discontinuous

15<latexit sha1_base64="+R1iRQNSRUNtdZWY/N5uC3cAJSw=">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</latexit>
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sha1_base64="vmpJEvxGQlYtvO3wTLFTr67zA6Y=">AAACi3ichVE9S8NQFD2N35+tugiCFIviVG78oCqCggiOtloVVEoSX2tomoQkLWhxdBFXdXBScBD/QHF1cXJz8CeIo4KLg7dJUUSsN+S9c8+7577zuKpt6K5H9BSSGhqbmlta29o7Oru6w5Ge3jXXKjqaSGuWYTkbquIKQzdF2tM9Q2zYjlAKqiHW1fxC9Xy9JBxXt8xVb88W2wUlZ+pZXVM8plLyZCYSozj5Ef0N5BqIzT1Uki+Hg5VlK3KLLezAgoYiChAw4TE2oMDlbxMyCDZz2ygz5zDS/XOBA7SztshVgisUZvO85jjbrLEm59Werq/W+BaDf4eVUQzTI13TK93TDT3Tx5+9yn6Pqpc93tVAK+xM+Kh/5f1fVYF3D7vfqrqePWQx5XvV2bvtM9VXaIG+tH/2ujKTGi6P0CW9sP8LeqI7foFZetOukiJ1XsePyu9WOBfc88Af07Qf0QAkJmpgWv4a09pYXKa4nKTY/BKCaMUAhjDKU0lgHktYRppvyeIYJziVuqRxaUaaDUqlUE3Thx8hLX4CkvKWlg==</latexit>

10
10

55
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sha1_base64="i2zVQl/szgRRbP5DILCcFRoxJaY=">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</latexit>
sha1_base64="ZIr4Tgpu/9Gqy9RFvbi3QFcFn6g=">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</latexit>
sha1_base64="IpFtH4k5CYuaIory+Zj756zX4vc=">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</latexit>

000.0
0.0
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0.2
0.2<latexit sha1_base64="i+k2mJiFb4HOdnS3Lf4PjD78y9g=">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</latexit>
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0.4
0.4<latexit sha1_base64="NqL8hbDmiSV4H2SDYabxZ5BPbeA=">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</latexit>
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0.6
0.6<latexit sha1_base64="HEM9OPMrHTrAY8pFV54ERnAvpbs=">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</latexit>
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J

0.8
0.8
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sha1_base64="NZt+LVGH4orrtZmejEgAQzjU3eY=">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</latexit>

1.2
1.2

1.0
1.0
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sha1_base64="bVhutuWGzC8wjDmG6ulfDazCK/g=">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</latexit>J

discontinuous

15
15

10
10

Bending Branch
BendingbranchFlat BranchFlatbranch<latexit sha1_base64="tSDDFT0a9e5oVORhCoY7tww7b4I=">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</latexit>
sha1_base64="3rq8M/AOIA8RV1MzwKX6exjj1y4=">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</latexit>
sha1_base64="kQjVxYC2jA7WXImy9uNgV3iz8gs=">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</latexit>
sha1_base64="cbFpInE5wFS8rDSRdx1qrf/ybbA=">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</latexit>

B=19

25
25

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sha1_base64="Rj0VZDs/9zerVEUEKO0VbH6jyOA=">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</latexit>
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sha1_base64="xNXjApXqWAM2Ii/v34JH/vLZpFE=">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</latexit>

15

(b)

30
30
F̃D

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55

1.4
1.4

000 0
0.0

02
0.2

04
0.4

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35
35

B=20
F̃D

20
20

J

15

12
1.2

10
1.0

14
1.4

B=21

25
25

20
20

J

15
15

15

10
10

10
10

continuous

55
000 0
0.0

(d)

J

08
0.8

hq̄qi

25
25

hq̄qi

30
30

06
0.6

F̃D

35
35

(c)
30
30

F̃D

J vs Chiral condensate

02
0.2

04
0.4

06
0.6

J

08
0.8

10
1.0

12
1.2

continuous

55
14
1.4

000 0
0.0

02
0.2

04
0.4

06
0.6

J

08
0.8

10
1.0

12
1.2

14
1.4

When B becomes larger, the chiral condensate in the bending branch is changed frommulti-valued to single valued.
The discontinuous jump of the chiral condensate is changed to the continuous transition.

Phase diagram
22
22

us
o
u
ti n
n
co

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er
d
r
d-o
n
2

SO(2) broken

20
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BCEP
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sha1_base64="p/A+6Atx+w9dMp2my+Pqpyfwo3o=">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</latexit>

B

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18
18

<latexit sha1_base64="uW6Yow3pZKKyZS1xCG5E1UBp9cA=">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</latexit>
sha1_base64="Thou+MZ0vyEBGC6zYCUVoZ2ahyI=">AAACi3ichVE9SwNBEH05v2L8itoINsGgWIW5WChiERAhpUZjBBW5Ozd65L642wQ05A+IrVpYKViI/8DWxj9gkZ8glhFsLJxcDkRFnWV3Z97Om33D6J5lBpKoGVO6unt6++L9iYHBoeGR5OjYZuBWfUMUDddy/S1dC4RlOqIoTWmJLc8Xmq1boqRXltvvpZrwA9N1NuSRJ3Zt7cAxy6ahSYYK6sJeMk0ZCi3101EjJ43IVt3kPXawDxcGqrAh4ECyb0FDwGsbKggeY7uoM+azZ4bvAg0kmFvlLMEZGqMVPg842o5Qh+N2zSBkG/yLxdtnZgrT9ES31KJHuqNnev+1Vj2s0dZyxLfe4Qpvb+RkYv3tX5bNt8ThJ+tPzRJlLIRaTdbuhUi7C6PDrx1ftNYXC9P1GbqmF9Z/RU164A6c2qtxsyYKl3/o0blvjWPBNRs8JvX7UH46m9mMShl1LZvO5aOBxTGJKczyVOaRQx6rKPIvZZziDOfKkDKnLCpLnVQlFnHG8cWUlQ+7cZGv</latexit>

t1s

16

Critical phenomena?

ph
r
e
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Flat branch<latexit sha1_base64="W2Jro5JQxtsmsukT49ykRhxBzNw=">AAAClHichVG9SgNBEJ6c//EnUUEEm2CIWIW5NIpYCKKkEk2MBmKQvXWTLLncHXebgIa8gL1YCIqChfgGtja+gIWPIJYKNhZOLgeiQZ1jb2e+nW/2mx3DMaWnEJ9CWk9vX//A4FB4eGR0LBIdn9jx7LrLRY7bpu3mDeYJU1oip6QyRd5xBasZptg1qqvt892GcD1pW9vq0BHFGitbsiQ5UwQV1k2mYobLLF7Zj8Yxib7Fuh09cOIQ2KYdvYM9OAAbONShBgIsUOSbwMCjrwA6I

16

0.0
0.0

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sha1_base64="QCSkzK/H05vtRyrIbkkHbMiqwXM=">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</latexit>SO(2) preserved

Bbend<latexit sha1_base64="iNxM9uQLyDRNQ7ANOt6pI+k6rjY=">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</latexit>
sha1_base64="ECps45EfrZWkqAQvukFrgD+CL/E=">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</latexit>

0.2
0.2

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sha1_base64="fNUPAqToWIwWWKwQhfY5lzyzM20=">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</latexit>

0.4
0.4

<latexit sha1_base64="NqL8hbDmiSV4H2SDYabxZ5BPbeA=">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</latexit>
sha1_base64="ihqY/O7pcJRAVuaW7GneXO2NwwE=">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</latexit>

0.6
0.6

<latexit sha1_base64="HEM9OPMrHTrAY8pFV54ERnAvpbs=">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</latexit>
sha1_base64="Mi+ySWjgsnFnHu9oMKKpfvEatdg=">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</latexit>

J

0.8
0.8

<latexit sha1_base64="b82s74hFpnaNwqLrNbaceoqf++4=">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</latexit>
sha1_base64="NZt+LVGH4orrtZmejEgAQzjU3eY=">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</latexit>

1.0
1.0

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1.2
1.2

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sha1_base64="8wwWStxtZTYkZqR6i+7WGtzvRGA=">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</latexit>

If we control the current density at given B, the symmetry is spontaneously broken.

Critical exponent
35

B=20.230

We define and calculate thecritical exponent near the criticalvalue of the current density.

hq̄qi

25

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20
15
10

Jc

5

6

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0.2

0.4

0.6

0.8

1.0

1.2

J
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5

1.4

4
3

hq̄qi

0
0.0

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Jc |



 : critical exponent<latexit sha1_base64="N3JZnNSX9vAWzGgYYAWTkKvC90A=">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</latexit><latexit
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Jc : critical value of the current density<latexit sha1_base64="j9GPou+dse23C6xPbUrGYebWSdg=">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</latexit>
sha1_base64="2Mk/ZGOWWElOGgiTj14bY+iYKpI=">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</latexit>

1
1. × 10-4

2. × 10-4|J<latexit sha1_base64="XT4+2JOB5usxspz9UoAifGv1SNQ=">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</latexit>
sha1_base64="eMw4MVmB1SGWEaxt0drFlNzjUaU=">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</latexit>

5. × 10-4

Jc |

0.001

0.002

1
=
2
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sha1_base64="nSSzZu5F3j5ocSECNkAHEvk8c+I=">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</latexit>

Critical exponent66
55 (a)
44

77
66
55

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sha1_base64="ES9iFkf7uM4vQr9+Z9hkjHJ0MEM=">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</latexit><latexit sha1_base64="95D2+Njs4ub79mOtCbgbP5iAjcM=">AAACjHichVE9S8NQFD2NX/W76iK4FEulLuV
sha1_base64="e4hpuvMYwkwOfzXagbcG9zhh4LY=">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</latexit>
sha1_base64="eCDdjK2gB76miNq6fXPZqmH7muk=">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</latexit>
sha1_base64="GW0HqWjDdTLmt2L72y2dPsxXxik=">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</latexit>

B=20.2

33

44

hq̄qi

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sha1_base64="QjHA9WDhEoLBMxvQfEYb/Xg89W8=">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</latexit>

33

B=20.3(b)hq̄qi<latexit sha1_base64="B0VwMowMJBZKnaEgBC+U/OTpT9s=">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</latexit><latexit
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22
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1. × 10-40.0001<latexit sha1_base64="hrI0xCwa43XoI3Vw641QXuWCXOw=">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</latexit>
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2. × 10-40.0002<latexit sha1_base64="kdPwb374vpjw2WtajKvR05xNXdM=">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</latexit>
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5. × 10-40.0005J<latexit sha1_base64="QZrCM3hF3IcuI55vGmMPoJMm2nI=">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</latexit>
sha1_base64="FuDIxG5NNkm3DhCvK2RoBx8j0ec=">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</latexit>
sha1_base64="AWyEjzfHSCAAvAKcdNN7pFBBmUE=">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</latexit>
sha1_base64="rPOcmbyA6l/zOPktPUkPt73XgSs=">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</latexit>

Jc<latexit sha1_base64="yTgXYCb+0S8aWpUUQD53mSVTdko=">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</latexit>
sha1_base64="f74f9Q9PNnSMa+I68U5yFl99yNk=">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</latexit>
sha1_base64="8i+QnAY6e0s/MZcs6gFCYiZnUV8=">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</latexit>
sha1_base64="y6ycgQEacY0gALT1rvtFnLNuh6c=">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</latexit>

0.001
0.001
<latexit sha1_base64="7/GQ9h3cSQQ6MA2e3J7Uts6OI/M=">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</latexit>
sha1_base64="SrXVtk6aeSsFOUs5FwrA7fy1M8k=">AAACjnichVE9S8NgEH4av7+rLoKLWCpO5eKgIogFl47VWi3UUpL4Vl+aJiFJC1r8Ay6OKk4KDuI/cNXBP+Dg6CiOCi4OXtKCaLFeyHt3z3vPvc9xumNKzyd6iigdnV3dPb19/QODQ8Mj0dGxTc+uuobIGrZpuzld84QpLZH1pW+KnOMKraKbYksvrwb3WzXhetK2Nvx9RxQq2q4lS9LQfIaylCBSi9FY4AObag3UZhBbuT94TgJI29FbbGMHNgxUUYGABZ9jExo8/vJQQXAYK6DOmMuRDO8FDtHP3CpXCa7QGC3zuctZvolanAc9vZBt8Csm/y4zpxCnR7qmN3qgG3qhzz971cMegZZ99nqDK5ziyNFE5uNfVoW9j71vVlvNPkpYDLVK1u6ESDCF0eDXDk7eMkvr8foMXdIr67+gJ7rjCazau3G1JtbP2+jReW6Nc8E9D3lN6u+ltAabcwmVEuoaxZLBsgLrxSSmMctbWUASKaSR5VckjnGKMyWqzCvLykqjVIk0OeP4YUrqC3xmlOc=</latexit>
sha1_base64="EI/9J2zClY4wg3TNZdwlJG67oCo=">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</latexit>
sha1_base64="DL85w0XSuuS5jw28D2+or5xBPhU=">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</latexit>

0.002
0.002

20
2.0
15
1.5

0 001
0.001
Jc

5 × 100.0005<latexit sha1_base64="FN+ynKa9la4WLCK6KbKAR01KOV8=">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</latexit>
sha1_base64="Nn+JKf5+fItfwk0QTWBupXrZSHA=">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</latexit>
sha1_base64="AVDktTcYGpyI73x8b1Tz5hrDiwM=">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</latexit>
sha1_base64="9MOf0SVzD28ZMR27UONY3SlRwDQ=">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</latexit>

0 002
0.002

0 005
0.005

J

2 50
2.5

(c)

B=23

2 25

(d)

2 00
2.0

10
1.0

B=30

hq̄qi

hq̄qi

1 75
1 50
1.5

05
0.5

1 25

1 × 100.0001

2 × 100.0002

Jc

5 × 100.0005
J

0 001
0.001

0 002
0.002

1.0
1 00
0 001
0.001

0 002
0.002
Jc

0 003
0.003

0 004 0.005
0 005 0 006
0.004

J

 = 1/2 is always satisfied along the 2nd-order phase transition line.

Analytical approach
350

J = (2⇡↵ )30

2|gtt |gxx= G(z⇤ ) cos3 ✓(z⇤ )

25

hq̄qi

p

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sha1_base64="JLDAipgMxhQeMRiQIUVW2HTVXvU=">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</latexit>

z=z⇤

cos3 ✓(z⇤ )20<latexit sha1_base64="4GuRtI/s7j5EIgGpWVXDZ3owQqw=">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</latexit>
sha1_base64="q/LZV6lmIIryyryf9drntbAjN4Y=">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</latexit>✓(z⇤ ) ⌧ 1

15<latexit sha1_base64="+FWBuoyUMBi36DOowWBgSsNnzCM=">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</latexit>
sha1_base64="qzUdZWCwPaOeIAsp97MdeBwaWjM=">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</latexit>

✓

10
5
0
0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

J

J ⇠ G(z⇤ ) 1✓= G(z⇤ ) 1<latexit sha1_base64="bZDG20AVcnjb1nN66AkZN+pfQn4=">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</latexit>
sha1_base64="oAxKvL1GvSG9JZ6bdZJWHyAN+uI=">AAADHHichVFLaxRBEK4ZX8n6yCZeAiI0LllXxaUmEQwBIeDB4CkPNwmk49LT6d1tMi9meheSYf6AN08eBEHBg/gPvOpBEI8K+QniMUIuHqyZHRCzJNbQ01Vf1fd1FeVGnk4M4oFlnzl77vyFsfHKxUuXr0xUJ6fWk7AfS9WSoRfGm65IlKcD1TLaeGozipXwXU9tuLsP8/zGQMWJDoMnZi9S277oBrqjpTAEtavPH9d5on32qLHfTm9ntxj3VMc0mMPuMt6JhUy56SkjyvTTdDbL6NxhXO6EJmE81t2eIXwuY5xX6g9OFprLiSNqx5VYu1rDJhbGRh2ndGpQ2nJY/QAcdiAECX3wQUEAhnwPBCT0bYEDCBFh25ASFpOni7yCDCrE7VOVogpB6C79uxRtlWhAca6ZFGxJr3h0YmIymMFv+A4P8TO+xx/4+0SttNDIe9mj2x1yVdSeeDa9dvRflk+3gd5f1qk9G+jAfNGrpt6jAsmnkEP+YP/F4drC6kxaxzf4k/p/jQf4kSYIBr/k2xW1+vKUflyaW1CsSDOjNTnHlzLqrM82HWw6K/dqi0vlwsbgGtyABm3lPizCEixDi145sq5bdeum/cr+ZH+xvw5LbavkXIV/zP7+B7OAxHY=</latexit><latexit sha1_base64="NKgAvfwVooY86kLGN86ilkULUEo=">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</latexit><latexit
sha1_base64="LrotO/+R83LXGSd4BnzPEutb3rE=">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</latexit>

2◆3✓(z⇤ )+ ···2◆3✓(z⇤ )2 + · · ·2In the limit of ✓(z⇤ ) ! 0 , J = Jc .
<latexit sha1_base64="fS71uf2JXXVKc/a/iyFp8Qufn6A=">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</latexit>
sha1_base64="BZ1pFb3hUJacWHVTIec1xlF0/Jk=">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</latexit><latexit sha1_base64="v41IJxtzP2Z8oC/3tJxxgdlvKRg=">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</latexit>
sha1_base64="g4XzkfEjXp/X4tilkgsfCgn6QHQ=">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</latexit>

J = Jc + a2 ✓(z⇤ )2 + a4 ✓(z⇤ )4 + · · ·<latexit sha1_base64="kGDat+OKZeu6rmUMCdqlLm/iZ4Q=">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</latexit>
sha1_base64="YGbcRok/O5S4vQP4QJlPOA/gG24=">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</latexit>

The current density is written as the even function of ✓(z⇤ ) .
<latexit sha1_base64="DNqc1jRmkTvgYrOijw7AiN1D5ew=">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</latexit>
sha1_base64="EpLBrtqKhqx1p1TkxCcYaeySdFU=">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</latexit>

Analytical approachOn the other hand, the chiral condensate is obtained from theasymptotic form of the ✓(z) near the AdS boundary z=0.
<latexit sha1_base64="cInip6bwmXkLSFgY7JvoCHkNfAA=">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</latexit>
sha1_base64="g+frR7tpgVF8odmB53duVuYDwug=">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</latexit>✓(z) = mz + ✓2 z 3 + · · ·<latexit sha1_base64="TKVeYjVgKJX3dg9PE3yG08PqawA=">AAACtXichVE9SxxRFD2On/Fzo42Q5pHFYBSWOypsFATBxtKPrAruZpmZfbsOzhczbxfcYf+AlZ2FVYQUIX2KNAo2+QMp/AkhpYKNRe7ODAkiMXeY98497577zuOagWNHiuimR+vt6x8YHHoxPDI6Nj6Rezm5G/nN0JIly3f8cN80IunYniwpWzlyPwil4ZqO3DOP1rvney0ZRrbvvVfHgay4RsOz67ZlKKaqubmyOpTKmG2/FavCFW0xL1KmGi90RPtDvNgR82Wr5quomstTgZIQT4GegTyy2PRz31BGDT4sNOFCwoNi7MBAxN8BdBAC5iqImQsZ2cm5RAfDrG1yleQKg9kjXhucHWSsx3m3Z5SoLb7F4T9kpcAM/aDPdEvf6Qv9pId/9oqTHl0vx7ybqVYG1YmT6Z37/6pc3hUO/6qe9axQx7vEq83eg4TpvsJK9a322e3OyvZM/IYu6Bf7/0g3dM0v8Fp31qctuX3+jB+T321wLrlnJxnTchIiBcWlDCzrf8a0u1DQqaBvLeXXNrKBDeEVXmOWp1LEGjawiRLfcoqvuMSVVtQqWk2rp6VaT6aZwqPQ/N/VP6Gn</latexit>
sha1_base64="uEbes2As92nSCkoNkLQwNaQH7YQ=">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</latexit>

1.4

Bending Branch
Flat Branch

1.2
1.0
0.8
0.6

✓(z)

0.4

<latexit sha1_base64="cInip6bwmXkLSFgY7JvoCHkNfAA=">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</latexit>
sha1_base64="g+frR7tpgVF8odmB53duVuYDwug=">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</latexit>

0.2
0.0

0

1

z = z⇤

2

3

4

5

6

AdS boundary

z=0<latexit sha1_base64="S8RuaMvvmw5VY3Uk60vywHdHagM=">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</latexit>
sha1_base64="imiiioJzpNG9YE8Z38vV0Df7LB8=">AAACjHichVG7SgNRED2u71eM2gg2YlCswqwEFEUICGJpEmMCGsLuehMX98XuJhBDfkCw1cJKwUL8A1sbf8DCTxBLBRsLZzcLosE4l3vvzLlz5p5hVMfQPZ/ouUfq7esfGBwaHhkdG49NxCen9jy75moir9mG7RZVxROGbom8r/uGKDquUEzVEAX1eDN4L9SF6+m2tes3HFEylaqlV3RN8RnKnWxQOZ6gJIU21+nIkZNAZDt2/B4HOIQNDTWYELDgs29AgcdrHzIIDmMlNBlz2dPDd4EWRphb4yzBGQqjx3xWOdqPUIvjoKYXsjX+xeDtMnMOC/REt/RGj3RHL/T5Z61mWCPQ0uBbbXOFU544ncl9/Msy+fZx9M3qqtlHBauhVp21OyESdKG1+fWTi7fcWnahuUjX9Mr6r+iZHrgDq/6u3WRE9rKLHpX7VjgWXLPFY5J/D6XT2VtOypSUM6lEejsa2BBmMY8lnsoK0tjGDvL8SxVnOMeFFJNS0rq00U6VeiLONH6YtPUF8VySOQ==</latexit><latexit sha1_base64="x68XzYpaB/33D9/9KHde8zaKu94=">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</latexit>
sha1_base64="zxW09SW7zmT8Ch/b9D+tHEhGlmQ=">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</latexit>

If we switch the sign of ✓(z) , the sign of the chiral condensate
must also be switched.
<latexit sha1_base64="cInip6bwmXkLSFgY7JvoCHkNfAA=">AAACknichVG7SgNBFD2u73d8FIJNMES0CXdF8FEpaSws1BgTiSK760QX98XuJKAhP2BrYaEWChbiH9ja+AMW+QSxVLCx8GazKCLqXXbm3DP33DnD1T3LDCRRrUlpbmlta+/o7Oru6e3rjw0MbgRuyTdE1nAt18/rWiAs0xFZaUpL5D1faLZuiZx+kK6f58rCD0zXWZeHnti2tT3HLJqGJpna3JL7QmoTR5M7sQSlKIz4T6BGIIEoVtzYHbawCxcGSrAh4EAytqAh4K8AFQSPuW1UmPMZmeG5QBVdrC1xleAKjdkDXvc4K0Ssw3m9ZxCqDb7F4t9nZRxJeqQbeqEHuqUnev+1VyXsUfdyyLve0Apvp/94JPP2r8rmXWL/S/WnZ4kiZkOvJnv3Qqb+CqOhLx+dvmTm15KVcbqiZ/Z/STW65xc45VfjelWsnf3hR+d3a5wL7lkNxzQXRrwBZqYjMKd+jmljKqVSSl2dTiwsRQPrwCjGMMFTmcEClrCCLN9i4wTnuFCGlXllUUk3SpWmSDOEb6EsfwAi2pVb</latexit>
sha1_base64="g+frR7tpgVF8odmB53duVuYDwug=">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</latexit>hq̄qi = b1 ✓(z⇤ ) + b3 ✓(z⇤ )3 + · · ·<latexit sha1_base64="RX9hNGb0shQwLPguy3e7bZbcHmQ=">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</latexit>
sha1_base64="3gxuP8lKeG7o0LeV8OJEEfA+kPI=">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</latexit>

Analytical approach
J = Jc + a2 ✓(z⇤ )2 + a4 ✓(z⇤ )4 + · · ·<latexit sha1_base64="kGDat+OKZeu6rmUMCdqlLm/iZ4Q=">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</latexit>
sha1_base64="YGbcRok/O5S4vQP4QJlPOA/gG24=">AAACzXichVFNS9xQFD3Gfqj9cGw3gpvQwWI7MNyIUCkIohtxUz86Kjg2vDyfGswkIXkzoGncCv4BF64UCi39B91205U7af0J4tJCNy68yQRKO9TekPfuPfee+87lOqHnxprovMvovnP33v2e3r4HDx897i8NPFmKg2YkVU0GXhCtOCJWnuurmna1p1bCSImG46llZ3s6yy+3VBS7gf9W74RqrSE2fXfDlUIzZJemZidm7USmFVPYyWhq1vWW0mJk105epi/eZUiFE2MdCUYqZl2uBzq2S2WqUm5mp2MVThmFzQWlL6hjHQEkmmhAwYdm34NAzN8qLBBCxtaQMBax5+Z5hRR9zG1yleIKweg2n5scrRaoz3HWM87Zkl/x+I+YaWKYzugTXdE3+kwXdP3PXkneI9Oyw7fT5qrQ7j8YXPz1X1aDb42t36xbNWtsYDzX6rL2MEeyKWSb39o9vFp8vTCcPKcTumT9x3ROX3kCv/VTfphXC0e36HF4bsGx4p4pr8n6eymdztJo1aKqNT9WnpwpFtaDITzDCG/lFSYxgznU+JWPOMV3/DDeGE3jvbHXLjW6Cs5T/GHG/g1tUqqi</latexit>hq̄qi = b1 ✓(z⇤ ) + b3 ✓(z⇤ )3 + · · ·<latexit sha1_base64="RX9hNGb0shQwLPguy3e7bZbcHmQ=">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</latexit>
sha1_base64="3gxuP8lKeG7o0LeV8OJEEfA+kPI=">AAAC2HichVG/axRBFP6yGo1JNBfTCDaLRyQaON6qEJEoAZs0Qn54SUg2LrObubshe7ub3bmDZFmwEy1tLKwULMTSztYm/4DFtVqJZQQbi7zdWwhJML5hZt775n1vvsdzI18lmqg3YJw7P3jh4tCl4ZHRy1fGKuNXV5KwE3uy7oV+GK+5IpG+CmRdK+3LtSiWou36ctXdfpy/r3ZlnKgweKp3I7nZFs1ANZQnNENO5Ynty4aeNW1XxOlOtmPasWq29CPzoeukVmbauiW1mNpz0tvZLXOawbsnwGc5Mm17W6FOnEqValSYedqxSqeK0hbCyhfY2EIIDx20IRFAs+9DIOG1AQuEiLFNpIzF7KniXSLDMHM7nCU5QzC6zWeTo40SDTjOayYF2+NffN4xM01M0jf6SAe0T5/oJ/39Z620qJFr2eXb7XNl5Iy9urb857+sNt8arSPWmZo1GrhfaFWsPSqQvAuvz+/uvTlYfrA0md6k9/SL9b+jHn3lDoLub+/Dolx6e4Yel/sWHEuumfGYrJNDOe2s3KlZVLMW71Xn5suBDeE6bmCKpzKDOcxjAXX+5TN6+I4fxrrx3HhhvOynGgMlZwLHzHh9CPrKr5Q=</latexit>hq̄qi ⇠ (Jc<latexit sha1_base64="pZ/Y0ci3M0vt4FAvcXjCSy1BU6M=">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</latexit>
sha1_base64="v/uxC4BDHfQYTKs8uI1ge774joU=">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</latexit>J)1/2 ( ✓(z⇤ ) ⌧ 1 )<latexit sha1_base64="+FWBuoyUMBi36DOowWBgSsNnzCM=">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</latexit>
sha1_base64="qzUdZWCwPaOeIAsp97MdeBwaWjM=">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</latexit>

Note that in this analytical discussion, we did not impose thecondition of B > BCEP .
<latexit sha1_base64="+g1SIOxJRamGjAuqNogQaNafXus=">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</latexit>
sha1_base64="CObdpxUd5oXOSC0ein6/u6hrbOw=">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</latexit>

Combined with the numerical results, it appears that the relationshipbetween the chiral condensate and the current density near B = BCEP
has the form of<latexit sha1_base64="Jm46cfKHBLqrgAfibGs/PYAI57k=">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</latexit>
sha1_base64="9HE2K1cje5xSUZmX/HOpQTp03ZY=">AAACk3ichVHLSsNQED3G97sqguCmWCquykQERRGkKrgR6qMPrFKSeFuDaRKStKDFH3AtuBAFBRfiH7h14w+48BPEZQU3LpykAVFR53LvnTl3ztwzjGobuusRPTVJzS2tbe0dnV3dPb19/ZGBwYxrVRxNpDXLsJycqrjC0E2R9nTPEDnbEUpZNURW3V/037NV4bi6ZW56B7bYKSslUy/qmuIxtJWcjyYLtcXl1FEhEqMEBRb96cihE0NoKStyh23swoKGCsoQMOGxb0CByysPGQSbsR3UGHPY04N3gSN0MbfCWYIzFEb3+SxxlA9Rk2O/phuwNf7F4O0wM4o4PdIN1emBbumZ3n+tVQtq+FoO+FYbXGEX+o9HNt7+ZZX59rD3yfpTs4ciZgKtOmu3A8TvQmvwq4en9Y3Z9XhtnK7ohfVf0hPdcwdm9VW7XhPrZ3/oUblvhWPBNf0xyd+H8tPJTCZkSshrU7GFlXBgHRjFGCZ4KtNYwApSSPMvJk5wjgtpWJqTktJSI1VqCjlD+GLS6genm5So</latexit>

J ⇠ Jc + c2 (B<latexit sha1_base64="6fRfAV9D9Z1paVvxtQG3U6qBHt8=">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</latexit>
sha1_base64="YvW7/JOikR4m+GLpnoCB941YCxI=">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</latexit>

BCEP ) hq̄qi

2c4 hq̄qi

0.03
0.03
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sha1_base64="DF7EwZZVtyvDm/Qn3KE+5Syfn0E=">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</latexit>
sha1_base64="xpHmrTo6QutnEWdwHEjYqnlCmSw=">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</latexit>

10

B = BCEP

B > BCEP

0.02
0.02<latexit sha1_base64="YlaP11PSJTlWbXru4NeMK/QTFsc=">AAACjXichVHLSsNQED3G97NVN4KbYlFclUlRakWk4EKXvvoAlZLEaxuaJiFJC1r8ARduK7hScCH+gVs3/oALP0FcVnDjwkkaFBHrhNw5c+6cuTOMahu66xE9d0ndPb19/QODQ8Mjo2OR6PhEzrVqjiaymmVYTkFVXGHopsh6umeIgu0IpaoaIq9W1vz7fF04rm6Zu96xLQ6qSsnUj3RN8XyKEpQsRuPsAov9BnII4ght04reYx+HsKChhioETHiMDShw+duDDILN3AEazDmM9OBe4BRDrK1xluAMhdkKnyWO9kLW5Niv6QZqjV8x+HdYGcMsPdEtteiR7uiFPv6s1Qhq+L0cs1fbWmEXI2dTO+//qqrsPZS/VR179nCEpaBXnXu3A8afQmvr6yfN1s7y9mxjjq7plfu/omd64AnM+pt2syW2Lzv0o/LcCseCa54Ga0oHFmuD1EII0vLXmnLJhEwJeYvimdVwYQOYxgzmeSspZLCBTWT5lTLO0cSFFJEWpRUpzJW6Qs0kfpi0/gn8u5Ke</latexit>
sha1_base64="XvJ6/Cq0SU5x8yJUdLkRgYuy7Nc=">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</latexit>
sha1_base64="BmLNbmp/rHf9z1nHVxNy7zZI3Ts=">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</latexit>
sha1_base64="HC1egz/tEwCdkGDLs+8tnAZ1Qus=">AAACjXichVHLSsNQED3G97NVN4KbYqm4KhMf+EC04EKXVm0rqEgSrxpMk5CkBS3+gAu3FVwpuBD/wK0bf8BFP0FcVnDjwsltUETUCblz5tw5c2cY3bVMPyCqNSnNLa1t7R2dXd09vX2xeP9A3ndKniFyhmM53qau+cIybZELzMASm64ntKJuiYJ+tBTeF8rC803H3giOXbFT1A5sc980tCCkKE3ju/EkO2mJn0CNQHLxYULaqhO/xzb24MBACUUI2AgYW9Dg87cFFQSXuR1UmPMYmfJe4BRdrC1xluAMjdkjPg842opYm+Owpi/VBr9i8e+xMoEUPdEt1emR7uiZ3n+tVZE1wl6O2esNrXB3Y2dD62//qorsAxx+qf7sOcA+ZmSvJvfuSiacwmjoyyfV+vrcWqoyStf0wv1fUY0eeAK7/GrcZMXa5R/96Dy3xrHgmqdyTbPSEg0wPRmBWfVzTfnxtEppNUvJzAIa1oFhjGCMtzKNDFawihy/cohzVHGhxJQpZV6JcpWmSDOIb6YsfwBaepTS</latexit>

hq̄qi

5
B > BCEP

2

J

1

0.01
0.01

0 005

Jc

J

0 010

0 015

0 020

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sha1_base64="EcMigEpBNHB7088rE8iAT9EVaNo=">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</latexit>
sha1_base64="jsGgmNLqGUWhyobQRoV2z9doCAE=">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</latexit>

Jc<latexit sha1_base64="q/Zev+zQfRlAWQuHeUaAO3Cxb/4=">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</latexit>
sha1_base64="zMRwdhpYRxnSSfnxNbU9H89GQPA=">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</latexit>
sha1_base64="0oYIjJn5nuMVfBHbq1IV2p35RVE=">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</latexit>
sha1_base64="MPJLr0sz/6n53O94Wn/pPF8EWBI=">AAACjXichVHLSsNQED2N72erbgQ3xaK4KhMf1IpowYUutVoVtJQkXjWYJiFJC1r8ARduFVwpuBD/wK0bf8BFP0FcKrhx4eQ2KCLqhNw5c+6cuTOM7lqmHxDVY0pTc0trW3tHZ1d3T2880de/7jsVzxAFw7Ecb1PXfGGZtigEZmCJTdcTWlm3xIZ+sBDeb1SF55uOvRYcuqJY1vZsc9c0tCCkKE1qKZFiJy35E6gRSM3fT0hbdhJ32MYOHBiooAwBGwFjCxp8/ragguAyV0SNOY+RKe8FjtHJ2gpnCc7QmD3gc4+jrYi1OQ5r+lJt8CsW/x4rkxihR7qhF3qgW3qi919r1WSNsJdD9npDK9xS/GRw9e1fVZl9gP0v1Z89B9jFtOzV5N5dyYRTGA199ejsZXUmP1IbpSt65v4vqU73PIFdfTWuV0T+4o9+dJ5b41hwzWO5pqy0ZANkJiOQVT/XtD6eVimtrlAqN4eGtWMIwxjjrWSQwxKWUeBX9nGKM5wrcWVKmVWiXCUWaQbwzZTFD1hUlNE=</latexit>

B = BCEP
0.00
0.00<latexit sha1_base64="6R8Pk++oZhwdztB9aR9WhdFwdJM=">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</latexit>
sha1_base64="g6S9HFLSiTF1PNBqwBXptdduMP0=">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</latexit>
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44

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hq̄qi
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J ⇠ Jc + c2 (BBCEP ) hq̄qi

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22
22

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1
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20
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Flat branch<latexit sha1_base64="W2Jro5JQxtsmsukT49ykRhxBzNw=">AAAClHichVG9SgNBEJ6c//EnUUEEm2CIWIW5NIpYCKKkEk2MBmKQvXWTLLncHXebgIa8gL1YCIqChfgGtja+gIWPIJYKNhZOLgeiQZ1jb2e+nW/2mx3DMaWnEJ9CWk9vX//A4FB4eGR0LBIdn9jx7LrLRY7bpu3mDeYJU1oip6QyRd5xBasZptg1qqvt892GcD1pW9vq0BHFGitbsiQ5UwQV1k2mYobLLF7Zj8Yxib7Fuh09cOIQ2KYdvYM9OAAbONShBgIsUOSbwMCjrwA6I

16

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Bbend<latexit sha1_base64="iNxM9uQLyDRNQ7ANOt6pI+k6rjY=">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</latexit>
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0.2
0.2

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0.4
0.4

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0.6
0.6

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J

0.8
0.8

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1.0

1.2

hq̄qi / |J

Jc |

1.0

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sha1_base64="8wwWStxtZTYkZqR6i+7WGtzvRGA=">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</latexit>Summary• We study the D3-D7 conducting system in the presence ofboth the electric field and the magnetic field.
• The non-equilibrium phase transition (spontaneously
symmetry breaking) occurs between the bending branch
and the flat branch.
• Two Remarks:
Ø Two branches are completely separated by the 1storder phase transition or the 2nd-order phasetransition.
Ø The critical exponent  is 1/2 at 2nd-order phasetransition point in or 1/4 at B=BCEP in our system.
<latexit sha1_base64="N3JZnNSX9vAWzGgYYAWTkKvC90A=">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</latexit><latexit
sha1_base64="8EPrbjHRBEBDVaOOF4Hcrshq7i4=">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</latexit>

Future perspective• Other critical exponents?
• Nambu-Goldstone mode?

Review: Landau theory and static criticalexponent in equilibrium phase transitions• Free energy near the critical point in ferromagnets
F = F0 + aM 2 + bM 4
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M : magnetization (order parameter)<latexit sha1_base64="y5Ifd6m0nukiJoLH1GRyb27uAx0=">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</latexit>

M / |TM / H 1/
/ |T<latexit sha1_base64="CRTVzgA7BRxXTlEJXUFRtiX9J/Y=">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</latexit>
sha1_base64="kM68C1RBWaVVP8VdmiGNXbKYAx0=">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</latexit>

Cv / |T

Tc |(T < Tc )H : external magnetic field• Static critical exponents(T = Tc )Tc |(T < Tc , T > Tc )Tc | ↵ (T < Tc )

1
,
2

=
<latexit sha1_base64="+QIA5Ij4y3aO9EmJGQTrrl7wWn4=">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</latexit>
sha1_base64="8OPRe1DQzSk1k1yt2kl117n1OTc=">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</latexit>
sha1_base64="i4pXsA52Dkmpx0K41T9VvdzMtVw=">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</latexit>= 3,= 1, ↵ = 0• Critical amplitude ratio
T > Tc / T < Tc =2<latexit sha1_base64="C8DGqpg9pOTgp0EqTll9fE01F2M=">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</latexit>=

Susceptibility :<latexit sha1_base64="LIQ1Z5JQaDqDeSM6bZqcL9U4Xow=">AAACh3ichVFNSxtBGH7c2qrph7G9CF6CQekpfdeDiiBYvOQi+NFEwYQwO52YIZvdZXcSsEvupX/AQ08KIiJ4be9e/AMe/AmlxxS8eOibzYLY0PYdZuaZZ97nnWdmnMDVkSG6HbGejD59NjY+kXn+4uWryezU63Lkt0OpStJ3/XDPEZFytadKRhtX7QWhEi3HVbtOc72/v9tRYaR974M5DFS1JQ48XddSGKZq2dmKbOjVSj0UMq4EIjRauLmN7gMudmvZPBUoidwwsFOQRxqbfvYMFXyED4k2WlDwYBi7EIi47cMGIWCuipi5kJFO9hW6yLC2zVmKMwSzTR4PeLWfsh6v+zWjRC35FJd7yMoc5uiGzqlH13RBP+j+r7XipEbfyyHPzkCrgtrkl+mdu/+qWjwbNB5U//RsUMdy4lWz9yBh+reQA33n01FvZ2V7Lp6nE/rJ/o/plq74Bl7nlzzdUttfkeEPsP987mFQXijYVLC3KL9WTL9iHDOYxVt+7yWsoYhNlPjcz7jEN3y3Jqx31qK1PEi1RlLNGzwK6/1vUd+XGg==</latexit>
sha1_base64="wIZSfE0bzzc9m1PTcaVbm/wa7aI=">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</latexit>
sha1_base64="ueeDwg+nfiDzHD1EOxTvnybsFEc=">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</latexit>

Specific heat : Cv =<latexit sha1_base64="QwuulDcH06hnF4x9FWYNc4pKMek=">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</latexit>
sha1_base64="/fawPKJY8krd6VoB2O78e/sBGM4=">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</latexit>
sha1_base64="5hRiHoIGIJPsZjGo8JVNKDlBxaI=">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</latexit>

@M
@H

@2F
T
@T 2

These values correspond with thosein the mean-field theory.