SLIDE 1
NG is NG?
ArXiv:1508.00433 Nambu and Science Fron3er 17 Nov. 2015
Koji Hashimoto (Osaka U) w/ Minoru Eto (Yamagata U)
Is internal space a space ?
NG is NG? Koji Hashimoto (Osaka U) w/ Minoru Eto (Yamagata U) - - PowerPoint PPT Presentation
NG is NG? Koji Hashimoto (Osaka U) w/ Minoru Eto (Yamagata U) - - PowerPoint PPT Presentation
Nambu and Science Fron3er 17 Nov. 2015 NG is NG? Koji Hashimoto (Osaka U) w/ Minoru Eto (Yamagata U) ArXiv:1508.00433 Is internal space a space ? Ques3on 1 Is internal space a space ? 1 page Method Generalized Soliton + 2 Mantons
SLIDE 2
SLIDE 3
Method
Is internal space a space ?
Ques3on Our answer
Can be.
1
1 page
3
3 pages
Generalized Manton’s method Soliton +
2
3 pages
We derive: generic ac3on
- f internal moduli
SLIDE 4
Is internal space a space ?
Ques3on
1
1 page
A) Target space on which global symmetry acts B) Compact extra dimensions A) In which a moving
- bject obeys rela3vity
B) In which a quan3zed field travels
SLIDE 5
Method
Is internal space a space ?
Ques3on Our answer
Can be.
1
1 page
3
3 pages
Generalized Manton’s method Soliton +
2
3 pages
We derive: generic ac3on
- f internal moduli
SLIDE 6
Soliton to view the space a la Manton
2-1
Domain wall effec3ve ac3on is Nambu-Goto
2-2
Nambu-Goto probes “space”
2-3
Method
Generalized Manton’s method Soliton +
2
3 pages
SLIDE 7
Soliton to view the space a la Manton
2-1
Domain wall effec3ve ac3on sees the space 1) Prepare a Scalar field ac3on 2) Obtain a domain wall solu3on 4 easy steps [Manton] 3) Upgrade moduli to a field 4) Subs3tute it back to the ac3on Domain wall
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Domain wall effec3ve ac3on is Nambu-Goto
2-2
Deriva3on Consider a Lorentz-transformed solu3on Subs3tute/evaluate it with general coordinate transf.
Using
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Nambu-Goto probes “space”
2-3
3 reasons for Nambu-Goto to see space3me 1) Ac3on = Rela3vis3c area (worldvolume) 2) General coordinate invariance 3) Speed of light in target space
◯ ◯ ◯
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Method
Generalized Manton’s method Soliton +
2
3 pages
Soliton to view the space a la Manton
2-1
Domain wall effec3ve ac3on is Nambu-Goto
2-2
Nambu-Goto probes “space”
2-3
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Method
Is internal space a space ?
Ques3on Our answer
Can be.
1
1 page
3
3 pages
Generalized Manton’s method Soliton +
2
3 pages
We derive: generic ac3on
- f internal moduli
SLIDE 12
Domain wall with internal U(1) moduli
3-1
Generic ac3on is a func3on of Nambu-Goto
3-2
To be a space
3-3
Our answer
Can be.
3
3 pages
We derive: generic ac3on
- f internal moduli
SLIDE 13
Domain wall with internal U(1) moduli
3-1
Internal moduli parameter of domain wall Generic complex scalar field theory Ex) Massive CP1 sigma model
φ1, φ2
Solu3on:
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Generic ac3on is a func3on of Nambu-Goto
3-2
Deriva3on 1) EOM:
= eimµxµ0
- z; m
- 1 + (µ)2
- 2) Domain wall solu3on: φ = eimcφ0 (z; m)
3) Exact solu3on w/ moving moduli 4) On-shell ac3on, iden3fy µ = µ(x)
g(m) ≡
- dz L
- φ=φ0(z;m)
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To be a space
3-3
1) Ac3on = Rela3vis3c area (worldvolume) 2) General coordinate invariance 3) Speed of light in target space
× ×
◯
( Scale invariance shows ) à Nambu-Goto ◯ ◯ ◯
g(m) ≡
- dz L
- φ=φ0(z;m)
φ0 = f(mz)
Excep3on:
SLIDE 16
Domain wall with internal U(1) moduli
3-1
Generic ac3on is a func3on of Nambu-Goto
3-2
Our answer
Can be.
3
3 pages
We derive: generic ac3on
- f internal moduli
To be a space
3-3
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Method
Is internal space a space ?
Ques3on Our answer
Can be.
1
1 page
3
3 pages
Generalized Manton’s method Soliton +
2
3 pages
We derive: generic ac3on
- f internal moduli
SLIDE 18
Speed limit in non-rela
A
Generic Non-rela3vis3c Lagrangian Solu3on with moving moduli Effec3ve ac3on Hamiltonian Upper bound only, no lower bound
- Cf. [Kobayashi,Nila]
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Generalized Nambu-Goto, monopoles, Higgs
Q
Q1) Massive CP1 + Poten3al = Double Sine-Gordon à Generalized Nambu-Goto Q2) ‘tHoon Polyakov monopole has U(1) moduli à Nambu-Goto [Tong] Speed limit consistent w/ CP1 Q3) Vacuum NG mode à No speed limit
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