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 Manton’s method 3 pages Our answer 3 We derive: generic ac3on Can be. of internal moduli 3 pages

Ques3on 1 Is internal space a space ? 1 page A) Target space on which A) In which a moving global symmetry acts object obeys rela3vity B) Compact B) In which a quan3zed extra dimensions field travels

Ques3on 1 Is internal space a space ? 1 page Method Generalized Soliton + 2 Manton’s method 3 pages Our answer 3 We derive: generic ac3on Can be. of internal moduli 3 pages

Method 2 -1 Soliton to view the space a la Manton Generalized Soliton + 2 Manton’s method 3 pages 2 -2 Domain wall effec3ve ac3on is Nambu-Goto 2 -3 Nambu-Goto probes “space”

2 -1 Soliton to view the space a la Manton Domain wall effec3ve ac3on sees the space 4 easy steps [Manton] 1) Prepare a Scalar field ac3on Domain 2) Obtain a domain wall solu3on wall 3) Upgrade moduli to a field 4) Subs3tute it back to the ac3on

2 -2 Domain wall effec3ve ac3on is Nambu-Goto Deriva3on Consider a Lorentz-transformed solu3on Subs3tute/evaluate it with general coordinate transf. Using

2 -3 Nambu-Goto probes “space” 3 reasons for Nambu-Goto to see space3me 1) Ac3on = Rela3vis3c area (worldvolume) ◯ 2) General coordinate invariance ◯ 3) Speed of light in target space ◯

Method Generalized Soliton + 2 Manton’s method 3 pages 2 -1 Soliton to view the space a la Manton 2 -2 Domain wall effec3ve ac3on is Nambu-Goto 2 -3 Nambu-Goto probes “space”

Ques3on 1 Is internal space a space ? 1 page Method Generalized Soliton + 2 Manton’s method 3 pages Our answer 3 We derive: generic ac3on Can be. of internal moduli 3 pages

3 -1 Domain wall with internal U(1) moduli 3 -2 Generic ac3on is a func3on of Nambu-Goto Our answer 3 We derive: generic ac3on 3 -3 To be a space Can be. of internal moduli 3 pages

3 -1 Domain wall with internal U(1) moduli Internal moduli parameter of domain wall Generic complex scalar field theory Ex) Massive CP 1 sigma model Solu3on: φ 1 , φ 2

3 -2 Generic ac3on is a func3on of Nambu-Goto � � � g ( m ) ≡ dz L � � φ = φ 0 ( z ; m ) Deriva3on 1) EOM: 2) Domain wall solu3on: φ = e imc φ 0 ( z ; m ) 3) Exact solu3on � � � � = e im � µ x µ � 0 z ; m 1 + ( � µ ) 2 w/ moving moduli 4) On-shell ac3on, iden3fy � µ = � µ � ( x )

3 -3 To be a space � � � g ( m ) ≡ dz L � � φ = φ 0 ( z ; m ) × 1) Ac3on = Rela3vis3c area (worldvolume) × 2) General coordinate invariance ◯ 3) Speed of light in target space Excep3on: à Nambu-Goto ◯ ◯ ◯ ( Scale invariance shows ) φ 0 = f ( mz )

Our answer 3 We derive: generic ac3on Can be. of internal moduli 3 pages 3 -1 Domain wall with internal U(1) moduli 3 -2 Generic ac3on is a func3on of Nambu-Goto 3 -3 To be a space

Ques3on 1 Is internal space a space ? 1 page Method Generalized Soliton + 2 Manton’s method 3 pages Our answer 3 We derive: generic ac3on Can be. of internal moduli 3 pages

A Speed limit in non-rela Upper bound only, no lower bound Generic Non-rela3vis3c Lagrangian Cf. [Kobayashi,Nila] Solu3on with moving moduli Hamiltonian Effec3ve ac3on � 0 �

Q Generalized Nambu-Goto, monopoles, Higgs Q1) Massive CP 1 + Poten3al = Double Sine-Gordon à Generalized Nambu-Goto Q2) ‘tHoon Polyakov monopole has U(1) moduli à Nambu-Goto [Tong] Speed limit consistent w/ CP 1 Q3) Vacuum NG mode à No speed limit