magnetars and domain walls - 名古屋大学hamanaka/hashimoto.pdf · 2014. 1. 6. · magnetars and...
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![Page 1: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/1.jpg)
Magnetars and Domain walls
Koji Hashimoto (Osaka / RIKEN)
Jan 05 2014 @Nagoya univ. workshop “Mathematics and physics on topological solitons”
Phys.Rev. D88 (2013) 081701 arXiv/1209.4814[hep-ph] + work in progress w/ M. Eto (Yamagata), T. Hatsuda (RIKEN)
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Discovery of astro-solitons?
![Page 3: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/3.jpg)
Problem Origin of magnetars?
Cause
No magnetization at high density hadron phase?
Our solution High density neutron matter
Axial anomaly + π0 domain wall
New phase : QCD Ferromagnetism
![Page 4: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/4.jpg)
~B
Parallel layers of domain walls
of neutral pion
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1. Magnetars. 2. Pion domain wall. 3. QCD Ferromagnetism.
4. Holographization.
Plan
3 pages
3 pages
5 pages
2 pages
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Observation of Magnetars
B = 3.2⇥ 1019pPP [G]
L = @t(I⌦2) / P /P 3
L = (2/3)m2 / B2/P 4
Spindown luminocity
Magnetic dipole assumption
[T.Enoto, 天文月報 2012.7] Magnetar hypothesis
Surface magnetic field
+
||
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Origin of the strong magnetic field?
[D.Page]
[Fukushima, Hatsuda 1005.4814]
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1. Magnetars. 2. Pion domain wall. 3. QCD Ferromagnetism.
4. Holographization.
Plan
3 pages
3 pages
5 pages
2 pages
--- What happens at the core?
![Page 10: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/10.jpg)
Weinberg’s action : nucleons and all pions
Chemical potential giving high density neutron matter
+
1
2
(@µ✓)2+ f2
⇡m2⇡(cos ✓ � 1)
L = n(i�µ@µ + µ�0 �Mn)n� 1
2f⇡(n�µ�5n)@
µ✓
Dµ ⌘@µ +
i
4f2⇡
(1 + �2/4f2⇡)
�1⌧ · (�⇥ @µ�)
�
Describing high density Chiral lagrangian for neutron and neutral pion
![Page 11: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/11.jpg)
Domain wall of neutral pion
Chiral lagrangian = Sine-Gordon model
L =
1
2
f2⇡(@µ✓)
2 �m2⇡f
2⇡ cos ✓
Domain wall solution
x
3✓(x)
�3 =2f⇡
sinh[m⇡x3]
�1 = �2 = 0
No topological obstruction against creation
✓(x)
�1,�2�3
S3
[Hatsuda 1986]
Classical solution connecting and ✓ = 2⇡✓ = 0
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Light domain wall in neutron matter
Integration of neutron at 1-loop à pion effective action modified
- Light domain wall
Neutron matter effect
L =
↵
2
(@0✓)2 � �
2
(@i✓)2+ f2
⇡m2⇡(cos ✓ � 1)
n
n
θ θ
[Hatsuda 1986]
1.02 1.04 1.06 1.08 1.10
0.2
0.4
0.6
0.8
1.0 �
µ/Mn
- β decreases at high density
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1. Magnetars. 2. Pion domain wall. 3. QCD Ferromagnetism.
4. Holographization.
Plan
3 pages
3 pages
5 pages
2 pages
--- What happens at the core?
--- Wall are light at high density
![Page 14: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/14.jpg)
Baryonically charged domain wall
QCD axial anomaly induces “ ” term, ⇡0 ! 2�
Domain wall inducing a baryon charge, under a magnetic field
Energy per baryon charge: If smaller than neutron mass, domain wall dominates!
[Son, Stephanov, 0710.1084]
Lanom
=e
4⇡2
µBB3
@3
✓~~~
~~~
θ q
q q
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Ferromagnetic QCD
Magnetization via wall
Induced baryon density :
Spontaneous magnetization. Very strong magnetic field,
QCD ferromagnetism
~B
Domain wall
layers B3 ⇠ 1019[G]
M =eµB
2⇡d
M =eµB
4⇡2@3✓
M =µB⇢
B3
[Son, Zhitnitsky, hep-ph/0405216]
Wall layer with interval : d
Equilibrium
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Issue 1) Spins align on the wall
n
n
pion �i�5@3✓
Si(x) = hn�i�5ni = (� � 1)f2⇡@i✓(x)
Neutron spins accumulate on the wall:
à Domain wall carries neutron spins:
Neutrons have magnetic moment :
Domain walls are magnetized:
[Hatsuda 1986]
µ =ges32Mn
with g ⇠ �3.8
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Issue 2) Eternal current at wall boundary Elemag + anomaly
EOM for A2
x1
x2x3
wall On the wall,
is nonzero, then wall boundary has effective eternal current
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Issue 3) Stability of the wall
The baryon charge induced is proportional to the area surrounded by the projected curve onto �1 = �2 = 0
The original domain wall is most effective, thus stable
�3 kinetic term does not cost energy +
The original wall has the largest charge
![Page 19: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/19.jpg)
1. Magnetars. 2. Pion domain wall. 3. QCD Ferromagnetism.
4. Holographization.
Plan
3 pages
3 pages
5 pages
2 pages
--- What happens at the core?
--- Wall are light at high density
--- Anomaly magnetizes the core
![Page 20: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/20.jpg)
Full meson theory (酒井杉本) giving the same
SD8 = � �Nc
216⇡3
Zd
4xdz (1 + z
2)F 2µz
AzPions are gauge field
Smass = c
Zd
4x Ptr exp
�i
Z 1
�1Azdz
�+ c.c.
Quark mass effect : worldsheet instanton
[Hirayama, Lin, Yee, KH 0803.4192] [Aharony, Kutasov, 0803.3547]
EOM for is solved as Aµ(x)
Then the EOM for reduces to sine-Gordon eq. of ✓(x)
Aµ = 0, Az =1
1 + z
2⌧3 ✓(x
µ)
Az(x)
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Anomaly analysis and Magnetization
Anomaly = CS term of the D8-brane action
SCS =Nc
24⇡2
Zd
4xdz A
(B)0 B
(em)3 @3Az.
Consider a chiral limit for light domain walls,
Az =1
1 + z
2ax
3
Total energy with all D8 action + EM :
= �Nc
✓a+
µqB
�
◆2
�Ncµ2
q
�B2 +B2
E ⇠ �Nca2 +NcµqBa+B2
µq >p
�/Nc à Spontaneous magnetization
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Problem Origin of magnetars?
Cause
No magnetization at high density hadron phase?
Our solution High density neutron matter
Axial anomaly + π0 domain wall
New phase : QCD Ferromagnetism
![Page 23: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/23.jpg)
Neutral pion domain walls
![Page 24: Magnetars and Domain walls - 名古屋大学hamanaka/Hashimoto.pdf · 2014. 1. 6. · Magnetars and Domain walls Koji Hashimoto (Osaka / RIKEN) Jan 05 2014 @Nagoya univ. workshop](https://reader033.vdocuments.mx/reader033/viewer/2022052615/608f9443152e0036952ac47b/html5/thumbnails/24.jpg)
More to come…
・Stability of the walls? Charged pion condensates
・Gravitational waves from isolated neutron stars?
・Neutron superfluidity? p-wave at high density, pairing on the walls
・Classification of neutron stars?
・EOS via walls?
[T.Enoto, 天文月報 (2012)]
・More realistic? Nuclear forces, hyperons