New dynamic criticalphenomena of nonrelativistic
photons in QCD
Noriyuki Sogabe（Keio University）
熱場の量子論 at YITP on September 4th, 2019in a collaboration with Naoki Yamamoto (Keio University)

Diﬀusion rate

Critical phenomena

Correlation length
Swinney and Henry (1973)

from Brookhaven National Laboratory

Dynamic universality class
P. C. Hohenberg and B. I. Halperin (1977)

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Dynamic universality class
P. C. Hohenberg and B. I. Halperin (1977)

Microscopic theory

Effective theory
Hydrodynamic variables:
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Same Symmetries-

Order parameters-

Conserved charge densities-

Nambu-Goldstone modes

Dynamic universality class
P. C. Hohenberg and B. I. Halperin (1977)

Gapless modes are important.

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nonrelativistic photon<latexit sha1_base64="x35057LjNBK7Olgb7XhB0/vrH0U=">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</latexit>k

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Todayʼs talkChirality and Quantum
anomaly• Chirality
spin

momentumright-handed: QR

left-handed: QL<latexit sha1_base64="j7Dpn70WrQOjAMzHLZUXJ1mWCDs=">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</latexit>
sha1_base64="E8CG8IEV8y5FJL1CKIFe/kpCAN8=">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</latexit><latexit sha1_base64="rQRrQo7y3xhZyzhYnzqfbB//SsU=">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</latexit>
sha1_base64="tFzxXb+imAQBulvS1/fDg2oSm2s=">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</latexit><latexit sha1_base64="7I/cOr3dp3cBpPDuVheTJd5ObTQ=">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</latexit>

Q5 ⌘ QR<latexit sha1_base64="S9toVikf57XJTv1lM974OLUXLaI=">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</latexit>

QL chirality charge

Q ⌘ QR + QL

total charge• Quantum anomaly<latexit sha1_base64="PJ2diqyxXc2mb+Hx71P5vMJLlzU=">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</latexit>@t n5 + r · j5 = CE · B

Outline• Setup• Static critical phenomena• Dynamic critical phenomena• Conclusion

Setup• Massless two-ﬂavor QCD at ﬁnite T and Bex• Chiral symmetry:<latexit sha1_base64="+HgVzg0Cfm6Low1NTC0Ei4KsJGE=">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</latexit><latexit sha1_base64="lz6/4edVwfKJX71aUkkSUn5Q8tc=">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</latexit>

Bex = 0<latexit sha1_base64="lqdAxcqGGHpN2crzcqPXN3k7Pgc=">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</latexit><latexit sha1_base64="c7qTT+Vn6LdLihFi0HWFtrWF1/U=">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</latexit>

SU(2)L ⇥ SU(2)R
◆
✓
u
q=
d
<latexit sha1_base64="S/FhqkVenfXnlxoMrmHMB+O0scs=">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</latexit>

U(1)<latexit sha1_base64="VIIrPhZqXR8u1hKh3UTs22weaa0=">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</latexit><latexit sha1_base64="yKzfMlIvd7XgmhGWVHnZgxb6WbY=">AAAG53icjZRLb9NAEICnAUwJj6ZwQeJiEYrgEm1aEIhTVFSpEpc+SFupbiPb3Sbb+BXbSZNa+QNcuAESpyJxQJz4C3DhDyDUGxwRxyJx4cB47CZNrMRdy+vZ2flmZme9qzmG8HzGjiYy585fkC5OXspevnL12lRu+vqaZzddnZd127DdDU31uCEsXvaFb/ANx+WqqRl8Xas/DefXW9z1hG099zsO3zLVqiV2ha76qKrknjUUV1Rrvuq69r6scHk7UISsqIZTU2XFV5vbc11ZHpqoPERNVTXNUOoZNSq5PCswanJSKMZCvnQHqC3Z05nPoMAO2KBDE0zgYIGPsgEqePhsQhEYOKjbggB1LkqC5jl0IYtsE604WqiorWNfxdFmrLVwHPr0iNYxioGvi6QMM+wb+8CO2Vf2kf1i/0b6CshHmEsHv1rEcqcy9eLm6t9UysSvD7U+NTZnH3bhMeUqMHeHNOEq9IhvHbw+Xn2yMhPcZe/Yb8z/kB2xL7gCq/VHf7/MV96OyUfDXEZXLMDIHFdooZUT21mo2aeqmbQOC/cpoN0S6KF7SnZovzoo+dj398al7JNeFKQC4l3UyTjqjompUH59az7WOrJrUX6hrBHjpjLtBNNOZRpDRCOV2MEnqly4s23sA9KMp8oJppzK1BPrqacyToJxUpn5BDN/Bob36h1RAVGVgV1Or//CkI+FVGIvke1eKnOA+sE4rMeM/sNPKnpyZ6l4LsbHCW+r01EijUZnKy1eaG2QNafzZ9FtKsjfPeLs2DaIPZh4Urtwn/xm8d4uDt/SSWFttlCcK8wuP8iXFqMLHCbhFtzGCEV4BCVYhCX8M3X4BN/hB/yUhPRSeiW9iUwzEzFzAwaadPgfQf1/Hg==</latexit>

ground stateBex 6= 0

q!e

⌧3

⌧3
⇥ U(1)5i↵⌧ 3 i↵5 5 ⌧ 3eU(1)<latexit sha1_base64="VIIrPhZqXR8u1hKh3UTs22weaa0=">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</latexit>q“isospin”• Second-order chiral phase transition<latexit sha1_base64="GQfrzEC/OOqtS+1LDPeZgX2JlEE=">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</latexit>⌧3⌧3⇥ U(1)5hq̄qi =
6 0

Hydrodynamic variables• (Complex) order parameter:<latexit sha1_base64="xrrKxAPuD6uLDB3BEm3bpNehCG4=">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</latexit>• Chirality charge density: n5<latexit sha1_base64="cYHrDGRCxvAWk0UMawE/PBUklnI=">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</latexit>• Electric ﬁeld: E<latexit sha1_base64="cGXdlXqOGl7BTWBOdoTLvvnh1Cs=">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</latexit>• Magnetic ﬁeld: B = Bex + B<latexit sha1_base64="0otVVmeGjr7L+RDLDHmrPcSI7s0=">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</latexit>⌘ hq̄qiGinzburg-Landau Theory
F =

Z ✓
V

<latexit sha1_base64="YiBVShJbI+W7vymbgAvO97HvUlM=">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</latexit>r 2 u 4 a
1 2 1 2 1 2
2| | + | | + |r | + n5 + E + B
2
4
2
2
2
2

◆

small order parameters• Near second-order phase transition
derivative expansion• Long-range behavior
constraints on the expansion• QCD symmetries
chiral symmetry and CPT symmetries

Ginzburg-Landau Theory
F =

Z ✓
V

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✓

⌧⌘

T

Tc
Tc

Wilson-Fisher ﬁxed point (2-components)◆◆

Dynamics• Preliminary= (h + h0 )ei⇡ 0 /h0<latexit sha1_base64="gVT40nL3C/yGvf8kzbHkAbkg9w8=">AAAGv3icjZTNbtNAEICnAUIJP23hgsTFIhS1QgqbggRCQgpFlXpMW9JWqtvIdrfJNv7Z2k5IauUB4AU4cAKJA+LAFa5w4QU49BEQxyJx4cB47DZNrNq15fXseL6Z2Rnv6tIUns/YwVju3PkL+YvjlwqXr1y9NjE5dX3Vc9quwWuGYzruuq553BQ2r/nCN/m6dLlm6SZf01vPw+9rHe56wrFf+D3JNy2tYYsdYWg+quqTRbXaFMpTRZlp3mvW2ayiqHwrUIWiSrHFlPuo66MVKzG6lKRQjoVi5Q7QVXWmct9AhW1wwIA2WMDBBh9lEzTw8N6AMjCQqNuEAHUuSoK+c+hDAdk2WnG00FDbwrGBs41Ya+M89OkRbWAUEx8XSQWm2U/2kR2yH+wT+8X+neorIB9hLj186xHLZX3i9c2Vv5mUhW8fmgMqNWcfduAx5Sowd0macBVGxHf23xyuPFmeDu6y9+w35v+OHbDvuAK788f4sMSX36bko2Mup1cswMgcV2ijlYztbNS8pKpZtA4b+xRQtwR66J+QJfWrh5KP46A3LmWf9KIiFRDvok7BWT8lpkr5Dax5qnVk16H8Qlknxs1kugmmm8nsjRB7mcQ23lHlws52cQxIk07VEkwtk2kl1tPKZGSCkZnMfIKZPwPDj+sdUQFR9aEuZ9d/YcTHQiaxm8h2N5PZR/1wHHbMnP6HH1X06MzScF+kxwlPq5NRIo1OeysrXmhtkjWn/WfTaSrI3wxxTmwbxB4s3Kl9mCW/BTy3y6OndFJYnSuVH5Tmlh4WK4vRAQ7jcAtuY4QyPIIKLEIV/0wDXsFn+AJf88/yjbydl5FpbixmbsDQle/9BykgbhA=</latexit>

Nambu-Goldstone mode
amplitude mode(linearly decoupled)

Langevin theory 1/20⇡• and n5<latexit sha1_base64="vM4KbVHoQRG/ZDCgP9HbQngqPpo=">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</latexit><latexit sha1_base64="h0HuEfiplYqxPpNbVMXg/bFV6SA=">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</latexit>0@t ⇡ =

F 0+⇡<latexit sha1_base64="HZ017q3vvQdoXG4IxHKXLjijCas=">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</latexit>@t n5 = r

2

F
+
n5

<latexit sha1_base64="0401fw10vYXTN71u1MQWP7z2J/8=">AAAHOnicjZRLb9NAEMcnBUIpj6ZwQeKyorQCFVWbAKJCQqqKinrsg6SVuo1lO5tkFWftOpuQ1PIX4Atw4AQSEoivwI0LZyQOvXKremwlLhwYr9OnScxatmfH/9/M7MNreY5oKUp3MyMXLl7KXh69Mnb12vUb47mJm6WW2/ZtXrRdx/U3LLPFHSF5UQnl8A3P52bTcvi61XgRfV/vcL8lXPlK9Ty+1TRrUlSFbSp0GbkfrGIoIo0nhEw/J8xBsmISJs1ygbCqb9oBq3BHmeRleGShOCQzhAmpDBKUQoIYr6pN9D9knihTwnxRq6stMigCiWXhzD9jLJZFagCCIoSwiq4gRqBLYtJVZo0xIzdJZ6luJGnk+8bk/D3QbdmdGPkEDCrggg1taAIHCQptB0xo4bUJeaDgoW8LAvT5aAn9nUMIY8i2UcVRYaK3gc8a9jb7Xon9KGZL0zZmcfD2kSQwRX/Sz/SAfqdf6B79MzBWoGNEtfTwbcUs94zxN7fXfqdSTXwrqJ9QQ2tWUIU5XavA2j3tiUZhx3xn5+3B2rPVqWCafqD7WP97uku/4Qhk59D+uMJX3w2px8JaBs9YgJk5jlCiyuvrJHpe61lr6nFIXKdAr5bACOEp29Pr1UNL4fNkbXxdfTIKQyrQvI8+gr1wSE6m6ztR86HqWNfR9UW2pRk/lekmmG4qs32O2E4lKnjFMxetbBefgfYMp4oJppjKNBLjaaQyXoLxUpmFBLPwHww/nu+YCjRlnFnl9PlfPBdjMZXYQf9Zhh4zg3fr0ewcnT8m7vHheaKT53SW2GPp/yQtX6R2tJrrf0nqk1HoePc15/a1QT9CE/+6EB7ouGN4BufPn7hJo1SYzT+aLaw8npxfig9jGIU7cBcz5OEpzMMSLOMuszNzmXKmlqlnv2Z/Zfey+7F0JNNnbsGZlj38C4XzoyI=</latexit><latexit sha1_base64="R2xvzFL6x/hsDqVcLSxkE4GcDNI=">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</latexit>

Z

⇥ 0
⇤ F
⇡ , n5+ ⇠⇡ 0
n5
V

Z

V

⇥

⇤ F
n5 , ⇡
+
0
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⇥ 0
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0
⇡ (t, r), n5 (t, r ) = h0 (r<latexit sha1_base64="khuUEsiDTKCfi0IO6JQV7FIvLOM=">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</latexit>

⇥

i

0

⇤

n5 (t, r), E (t, r ) = CBi (r

Z

V

⇥

⇤ F
n5 , E+ ⇠n5iEir 0 ) (tt0 )r 0 ) (tt0 )Anomalous commutation relation
S. Adler and D. Boulware (1969)

Langevin theory 2/2• Maxwell equations:<latexit sha1_base64="oOLneNYkcAQIIUR8z7MnNa+XJgY=">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</latexit>• Current term:@t E = r ⇥ B

j,@t B =r⇥EC
j = E + Cn5 B + r⇡ 0 ⇥ E + ⇠h0<latexit sha1_base64="pCa6DNS6ALXEIu/cusNXkpCbjPQ=">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</latexit>

Chiral magnetic eﬀect<latexit sha1_base64="PdUZaq6z8OlDTD7lBtHGDIpfDsU=">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</latexit>h⇠i (t, r)⇠j (t, r 0 )i = 2 ij (rr 0 ) (tt0 )Linear analysis• Linearize: B = Bex + B etc.
<latexit sha1_base64="BHjrxXV1rO7itO7CtoJQpP53TYA=">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</latexit>• Hydrodynamic (gapless) modes:-

1 diﬀusive mode
nonrelativistic photon:

!=±

s

v2
2
C 2 Bex2
D 2 k?

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D⌘ +
2
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2
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2
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From
statics:
0•<latexit sha1_base64="qzBUW0t/w6qrgrAo6dUNt7Rmm/E=">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</latexit>• Dynamic critical exponent:<latexit sha1_base64="2ZxeDW/rJD1rIyDiBOGOewl0XOM=">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</latexit>dz = +1
2

New dynamic universality classbeyond Hohenberg and Halperinʼs classiﬁcation

Conclusion• Dynamic critical phenomena of the second-order chiralphase transition under external magnetic ﬁeld withdynamical electromagnetic ﬁelds• Hydrodynamic modes: Nonrelativistic photon• New dynamic universality class beyond conventionalclassiﬁcation