Koji Hashimoto (Osaka U) w/ Minoru Eto (Yamagata U)

NambuandScienceFron3er17Nov.2015
NGisNG?
KojiHashimoto(OsakaU)
w/MinoruEto(YamagataU)
ArXiv:1508.00433
Isinternalspaceaspace?
Ques3on
Isinternalspaceaspace?
1
1 page
Method
Soliton
Generalized
Manton’smethod
+
2
3 pages
Our answer
Wederive:genericac3on
Canbe.
ofinternalmoduli
3
3 pages
Ques3on
Isinternalspaceaspace?
1
1 page
A)Targetspaceonwhich
globalsymmetryacts
B)  Compact
extradimensions
A)Inwhichamoving
objectobeysrela3vity
B)  Inwhichaquan3zed
fieldtravels
Ques3on
Isinternalspaceaspace?
1
1 page
Method
Soliton
Generalized
Manton’smethod
+
2
3 pages
Our answer
Wederive:genericac3on
Canbe.
ofinternalmoduli
3
3 pages
Method
2-1 SolitontoviewthespacealaManton
Soliton
Generalized
Manton’smethod
+
2
3 pages
2-2Domainwalleffec3veac3onisNambu-Goto
2-3
Nambu-Gotoprobes“space”
2-1
SolitontoviewthespacealaManton
Domainwalleffec3veac3onseesthespace
4easysteps[Manton]
1)PrepareaScalarfieldac3on
Domain
2)Obtainadomainwallsolu3on
wall
3)Upgrademodulitoafield
4)Subs3tuteitbacktotheac3on
2-2
Domainwalleffec3veac3onisNambu-Goto
Deriva3on
ConsideraLorentz-transformedsolu3on
Subs3tute/evaluateitwithgeneralcoordinatetransf.
Using
2-3
Nambu-Gotoprobes“space”
3reasonsforNambu-Gototoseespace3me
◯1)  Ac3on=Rela3vis3carea(worldvolume)
◯2)  Generalcoordinateinvariance
◯3)  Speedoflightintargetspace
Method
Soliton
2-1
Generalized
Manton’smethod
+
2
3 pages
SolitontoviewthespacealaManton
2-2Domainwalleffec3veac3onisNambu-Goto
2-3
Nambu-Gotoprobes“space”
Ques3on
Isinternalspaceaspace?
1
1 page
Method
Soliton
Generalized
Manton’smethod
+
2
3 pages
Our answer
Wederive:genericac3on
Canbe.
ofinternalmoduli
3
3 pages
3-1
DomainwallwithinternalU(1)moduli
3-2
Genericac3onisafunc3onofNambu-Goto
Our answer
Wederive:genericac3on
Tobeaspace
3-3 Canbe.
ofinternalmoduli
3
3 pages
3-1
DomainwallwithinternalU(1)moduli
Internalmoduliparameterofdomainwall
Genericcomplexscalarfieldtheory
Ex)MassiveCP1sigmamodel
Solu3on:
1,
2
3-2
Genericac3onisafunc3onofNambu-Goto
g(m)
dz L
=
0 (z;m)
Deriva3on
1)EOM:
2)Domainwallsolu3on: = eimc
0
(z; m)
3)Exactsolu3on
im µ xµ
=e
w/movingmoduli
0
z; m
4)On-shellac3on,iden3fy
µ
=
µ
(x)
1 + ( µ )2
3-3
Tobeaspace
g(m)
dz L
=
0 (z;m)
×1)  Ac3on=Rela3vis3carea(worldvolume)
×2)  Generalcoordinateinvariance
◯ 3)  Speedoflightintargetspace
Excep3on:
àNambu-Goto◯◯◯
(Scaleinvarianceshows)
0 = f (mz) Our answer
Wederive:genericac3on
Canbe.
ofinternalmoduli
3
3 pages
3-1
DomainwallwithinternalU(1)moduli
3-2
Genericac3onisafunc3onofNambu-Goto
3-3
Tobeaspace
Ques3on
Isinternalspaceaspace?
1
1 page
Method
Soliton
Generalized
Manton’smethod
+
2
3 pages
Our answer
Wederive:genericac3on
Canbe.
ofinternalmoduli
3
3 pages
A
Speedlimitinnon-rela
Upperboundonly,nolowerbound
GenericNon-rela3vis3cLagrangian Cf.[Kobayashi,Nila]
Solu3onwithmovingmoduli
Hamiltonian
Effec3veac3on
0
QGeneralizedNambu-Goto,monopoles,Higgs
Q1)MassiveCP1+Poten3al=DoubleSine-Gordon
àGeneralizedNambu-Goto
Q2)‘tHoonPolyakovmonopolehasU(1)moduli
àNambu-Goto [Tong]
Speedlimit
consistentw/CP1
Q3)VacuumNGmodeàNospeedlimit