magnetars and domain walls - 名古屋大学hamanaka/hashimoto.pdf · 2014. 1. 6. · magnetars and...
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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)
Discovery of astro-solitons?
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
~B
Parallel layers of domain walls
of neutral pion
1. Magnetars. 2. Pion domain wall. 3. QCD Ferromagnetism.
4. Holographization.
Plan
3 pages
3 pages
5 pages
2 pages
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
+
||
Origin of the strong magnetic field?
[D.Page]
[Fukushima, Hatsuda 1005.4814]
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?
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
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
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
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
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
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
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
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
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
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
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)
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
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
Neutral pion domain walls
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
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