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- りさこ みねむら
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1 D 2009 A * 1 ( ) *1 ( )
2 D D D D D D M1 6 D D M1 M2 D D 1
3 D D 6 1/2 π D D 6 M1 M1 D2 D M1 D3 string field theory 6 D chiral perturbation D D D 90 M1 2
4 95 D 15 D D D, (, 2006), ( BP, 2009) 5, (, 2007), (, 2005) A First Course in String Theory, Barton Zwiebach (Cambridge University Press, 2004) 1, 2, Joseph Polchinski, (, 2005, 2006) society
5 3 100 D 5 10 Zwiebach A first course in string theory D 3 D A first course in string theory D Polchinski String theory 1 Becker-Becker-Schwarz 4
6 D D D D D D 1 D 2 D 1 5
7 1 30 6
8 30 7
9 m m GeV 8
10 coupling e sector e, µ, τ e µ τ u c t d s b 9
11 10 4 order naturalness consistent naturalness Naturalness coupling naturalness naturalness naturalness [1, 2, 3] ( ) (1)
12 ( ) (2) naturalness 11
13 Randall N N
14 Newton F = G m 1m 2 r 2 m 1, m 2 r G c = 1, = 1 2 M pl = 1 G [GeV] 10 2 [GeV] 1 13
15 ϕ 4 1-loop Einstein Einstein 1-loop matter [4] *2 loop [8] *2 Einstein 1-loop Veltman Les Houches [5] Einstein-Maxwell [6] Einstein-Yang-Mills [7] 1-loop 14
16 Feynman graphical t = t 0 ϕ(t 0, x i ) t = t 1 ϕ(t 1, x i ) A = e is[ϕ] = Dϕe is[ϕ]/ (3) A amplitude 2 t = t 0 t = t 1 e is[ϕ] A 2 ϕ(t 0, x i ) ϕ(t 1, x i ) 15
17 δs δϕ = 0 eis[ϕ] X i (t = t 0 ) X i (t = t 1 ) δs δϕ = 0 *3 D *3, (, 2008) 16
18 ϕ 3 λ ϕ ϕ 3 λ λ λ order graph Feynman graph ϕ 3 λ A = Dϕe i ( ϕ ϕ+λϕ 3 ) ( = Dϕe i ϕ ϕ 1 + i ) λϕ 3 + (4) (5) graph 17
19 Feynman 18
20 λ coupling λ λ { ϕ(x) Zϕ(x) Z = 1 + c1 λ + c 2 λ 2 + λ Zλ Z = 1 + c1 λ + c 2 λ 2 + Einstein Einstein (6) 19
21 10 20
22 ( ) 21
23 22
24 23
25 λ λ α = e2 4πϵ 0 c = order (α s 1) 24
26 α α 25
27 u,d λ ϕ amplitude coupling 26
28 27
29 pure Yang-Mills mass gap Yang-Mills 28
30 L 1 L QCD L QCD QCD QCD 29
31 QCD 2 m 2 = 1 α J 1/α - 1/α α origin 30
32 QCD 5 31
33 bound state 32
34 X i (t) (i = 1, 2, 3) t d 2 dt 2 Xi (t) = 0 (7) 0 t X i (t) = a i t + b i, (a i, b i ) (8) 33
35 ( 1 S = dt 2 m d d ) dt Xi dt Xi + X i (t)f i (t) (9) d 2 X i /dt 2 (dx i /dt) 2 m X i F i F i i X i (t) 0 ( ( ) ) 2 1 d S = dt 2 m dt Xi + e dxi dt A i(x i (t)) A i (X i (t)) X i (t) A i (X i ) X i e e (10) 34
36 t t τ τ σ (τ, σ) (τ, σ) X µ X µ (τ, σ) (τ, σ) world sheet ( ) X µ X µ X µ µ d µ 0 d 1 (τ, σ) parametrization X µ trajectory sweep trajectory world sheet τ τ X 0 parametrization 35
37 σ boundary condition σ 0 2π σ = 0, 2π X µ σ 0 σ X µ σ=0,2π = 0 (11) fix fix D X µ (τ, σ + 2π) X µ (τ, σ) t 2 X µ = 0 (12) world sheet Lorentz σx 2 µ 0 t 2 X µ + σx 2 µ = 0 (13) 36
38 X µ = X µ L (τ + σ) + Xµ R (τ σ) (14) boundary condition X µ = x µ + l 2 sp µ τ + il s n Z,n 0 1 n αµ ne inτ cos nσ (15) l s l s cos nσ α n µ µ µ n = 1 cos (1 σ) n = 2 n = 3 µ µ µ *4 *4 Polchinski 37
39 τ ls 2 ( ) α n µ ( m 2 (= p µ p ν η µν ) = 1 ls ) nn n (16) n>0 p µ p ν η µν flat metric contract 1 l 1 + summation nn s 2 n N n n N n 0 [11] N massless state massless state N 1 α µ 1 µ µ A µ (x) 38
40 massless identify consistent 39
41 N1 L N 1 R 1 0 L R τ + σ τ σ α µ 1 left mover αµ 1 right mover 1 0 (µ, ν) g µν massless massless m m massless boundary condition hadron effective 40
42 2.2 world sheet world sheet ( ) ( ) 2 41
43 consistent [12, 13] 1-loop 42
44 Feynman ϕ ψ ϕ ψ λ 1, λ 2, λ 3 assign ϕ ψ Feynman coupling coupling g s g s g string g s coupling constant 43
45 boundary condition 2 Feynman deformation Feynman parameter region parameter region coupling constant Feynman g s (o) o open string g s (c) coupling constant coupling g s (c) c closed string coupling constant (g s (o) ) 2 = g s (c) (17) coupling constant Feynman 44
46 consistent (duality) tree diagram consistent electron coupling, coupling top quark coupling coupling constant constraint coupling loop momentum Feynman deform class worldsheet Feynman Feynman loop loop momentum worldsheet 45
47 QCD QCD loop QCD loop QCD QCD consistent loop loop QCD 46
48 2.3 critical dimension Lorentz Lagrangian 3 2 Lagrangian Lagrangian Lagrangian
49 X µ bosonic consistent X µ ψ µ Lagrangian critical dimension N = 2 critical dimension 4 4 N = 2 d =
50 Lorentz M µ ν Lorentz M ρσ generator M µ ν generator exp Lorentz generator M µν µ, ν ϵ ρσ Lorentz M µν Lorentz generator [ M µν, M ρσ ] = i(η µρ Mνσ η νρ Mµσ η µσ Mνρ + η νσ Mµρ ) (18) M ν µ M σ ρ M Lorentz Lorentz X µ µ Lorentz Lorentz M x M x x (19) X α n µ α n µ Lorentz anomaly Lorentz anomaly Lorentz critical dimension 49
51 critical dimension parameter M µν 0 X µ 50
52 x 1, x 2 x x 2 x 2 + 2πR x 2, 51
53 ϕ 2 x 1 x 2 ϕ(x 1, x 2 ) = ϕ(x 1, x 2 + 2πR) (20) Kaluza-Klein KK KK Kaluza-Klein
54 R R R R 53
55 10 critical dimension 10 ϕ(x µ ) ( ) ϕ(x µ ) = 0, (µ = 0,, 9) (21) 4 x 4 x 9 x i x i + 2πR i (i = 4,..., 9) [ 9 ( ϕ(x µ ) = ϕ s4...s 9 (x 0, x 1, x 2, x 3 si x i ) ] ) cos + c i (22) R i s 4,...s 9 Z,s 4,...s 9 0 ϕ(x µ ) x i x i + 2πR i ( si x i ) cos + c i (23) R i c i s i s i 1, 2, 3,... ϕ s4...s 9 x 0,..., x 3 s i s i s i 0 i=4 54
56 4 µ s i i=4 R i s i s 4 s 9 10 ϕ(x µ ) ϕ s4...s massless particle s i 0 1 R 4 R 9 R i R 1 R Kaluza-Klein 1 R 55
57 4 1 R 1 R 1 R 0 Kaluza-Klein LHC 1[TeV] Tera electron Volt [m] Kaluza-Klein 10 56
58 ( ) Kaluza-Klein 1 R 1 R ( ) 1 R x 1 R 2 1 R 57
59 Kaluza-Klein 1 R 10 g MN M, N = 0, 1,..., 9 4 M, N µ, ν g µν M, N i, j g ij µ, i g µi i, j i, j bi-gravity Higgs LHC Higgs R Kaluza-Klein LHC 58
60 spherical harmonics
61 S = 1 gs 2 d 10 x gr 1 (l s ) 8 (24) 1/(l s ) 8 d 10 x 10 gr 2 1/(l s ) 8 dimensionless 1/(l s ) 8 l s Einstein-Hilbert action S = 1 d 4 x gr G ( ) G G 1 g 2 s 1 (l s ) 8 V 6 = 1 G V 6 10 S = 1 g s (25) (26) d 10 sf µν F µν 1 (l s ) 6 (27) 60
62 1 g s 1 g s 2 1 g s open string coupling 2 closed string 1 g s F µν mass dimension 2 1 l 1 s 8 l s 6 4 coupling 1 e g s ls 6 V 6 = 1 e 2 (28) 2 l s V 6 61
63 l s ( ) 3 ( GV6 e 2 ) 4 V 6 = (29) g 2 s g s V 6 V 6 = G3 g 2 se 2 (30) V 6 R V 6 (2πR) 6, R R = 1 ( ) 1 G 3 6 2π gse 2 8 (31) G g s coupling constant g s 1 g s 1 coupling constant e 1 g s order estimate 1 G Plank 1 G Plank [GeV] order 0 order fluctuation 62
64 1 R 1 G 1 G Plank [GeV] LHC 10 Kaluza-Klein Kaluza-Klein Kaluza-Klein 63
65 10 1 D 64
66
67 2 solitary particle. 66
68 h x, y h = h(t, x, y) h [ 1 ( 2 ( ) 2 ( ) ] 2 v t) h + (h ) 0 (32) x y h 2 ϕ 4 h h kinetic term x, y, t argument 67
69 h h h h ϕ ( ) h(x, y, t) x y y x y 68
70 ϕ ϕ 3 kinetic term term λ λ ϕ ϕ ϕ 1/λ ϕ ϕ = 1 λ ϕ λ S = 1 λ 2 d 4 x( µ ϕ µ ϕ + ϕ3 ) (33) 1/λ 2 λ action overall λ 1/λ 2 action 1/λ 2 69
71 70
72 (1 + 1) ϕ explicit ϕ 4 V (ϕ) = λ 4 ) 2 (ϕ 2 + m2 (34) λ ϕ 4 ϕ 2 ϕ 4 ϕ 2 m 2 ϕ 4 λ ( ) ϕ = 0 ϕ = 0 ϕ ϕ 4 ϕ 2 ϕ ϕ ϕ ϕ 71
73 72
74 ϕ ϕ = 0 73
75 m 2 m 2 m m 2 (p57 ) ϕ = m m λ ϕ = λ ϕ ϕ 2 2 ϕ 2 ϕ ϕ 74
76 m 2 m 2 = E 2 p 2 m 2 m 2 < 0 p 2 = 0 v = p E m 2 2 ϕ ϕ = m λ + ϕ (35) ϕ m 2 consistent 75
77 x 0 ϕ cl (x 1 ) x 1 x 1 = p57 x 1 = + configuration x 1 = X 1 ( p59 ) x 1 ϕ ( p59 ) ϕ x 1 76
78 W x 1 -ϕ p59 p59 p59 77
79 ϕ cl tanh tanh argument x 1 X 1 tanh 1 +1 interpolate ( ) ( ) 78
80 x 1 Ax 1 + Bx 0 A B A 2 B 2 = 1 x 1 = X 1 exp M1 ( ) ( ) 79
81 ( ) ( ) λ QCD N = 2 SQCD [14, 15] constraint λ 80
82 (1 + 1) x 1 (1 + 2) x 1 y 1 y (1 + 3) x 1 x 2 x 3 81
83 ϕ 4 (1 + 1) trajectory (1 + 0) (1 + 2) sweep (1 + 1) (1 + 3) p62 membrane sweep (1 + 2) world volume( ) (1 + 4) (1 + p + 1) p p world sheet world volume (1 + p) p p p 1 + (p + 1) (1 + 4) p = 3 (1 + 3) 3 82
84 Kaluza-Klein Kaluza-Klein Kaluza-Klein R Kaluza-Klein
85 1 + 4 Kaluza-Klein ϕ cl = m [ ] m λ tanh (x 4 X 4 ) 2 x x 4 x 0 x 3 x 4 x 4 X x 4 x 0 x 3 ϕ cl X 4 X 4 x 0 x 3 kinetic term m X 4 ϕ cl m X 4 ϕ cl X4 =0 tanh X 4 (36) 84
86 [ ( 0 ) 2 + ( 1 ) 2 + ( 2 ) 2 + ( 3 ) 2] X 4 (x 0, x 1, x 2, x 3 ) = 0. (37) X 4 x 0 x 1 x 2 x massless particle massless moduli approximation massless X 4 85
87 X 4 X 4 ( ) x X 4 = X 4 (x 0, x 1, x 2, x 3 ) ( ) x 0 x 3 3 X 4 X 4 X 4 ϕ cl = m [ ] m λ tanh (x 4 X 4 ) (38) 2 X 4 X 4 tanh ϕ cl = m λ tanh m 2 x 4 m 2 2λ 1 [ ]X 4 + (39) cosh 2 m 2 x 4 X 4 = 0 tanh cosh 2 x 4 = 0 86
88 X 4 cosh 2 x 4 = 0 X 4 0 X 4 ϕ X 4 massless ϕ 4 massless massless X 4 X 4 massless global massless particle massless 87
89 D D D Kaluza-Klein Kaluza-Klein C 88
90 ϕ X 4 massless massive [16] ϕ cl δϕ δϕ cosh 2 sinh cosh 2 ψ ψ ϕ 4 3 m = 2 m massless massive ψ ψ [ ] [ ] ϕ = ϕ cl + δϕ sinh m 2 x 4 / cosh 2 m 2 x 4 *5 D *5 δϕ(x 0, x 1, x 2, x 3, x 4 ) = Y (x 4 )ψ(x 0, x 1, x 2, x 3 ) Y (x 4 ) 1 Schrödinger 89
91 constraint 90
92 D massless ϕ vortex
93 {, } ϕ { m, m } λ λ (40) x 1 ± {+, } {( ), ( )} ϕ x 1 non trivial + x x 2 2 = r r S 1 S 1 92
94 ϕ 4 x 1 x 2 ϕ ϕ 1 ϕ 2 λ m 2 ϕ 1 ϕ 2 ϕ 1 ϕ 2 V (ϕ 1, ϕ 2 ) = λ 4 ) 2 ((ϕ 1 ) 2 + (ϕ 2 ) 2 + m2 (41) λ m 2 (ϕ 1 ) 2 + (ϕ 2 ) 2 = ( ) S 1 S 1 S 1 93
95 ϕ 2 ϕ 1 + iϕ 2 ϕ 1 ϕ 2 action ϕ 1 = ( ), ϕ 2 = 0 (42) W 94
96 0 S 1 S 1 S
97 ϕ 4 anti-vortex 96
98 tanh 0 static kinetic term term ϕ 0 ϕ notation ( ( 1 ) 2 + ( 2 ) 2) ϕ λϕ ) ( ϕ 2 + m2 = 0 (43) λ ansatz ansatz ϕ(r, θ) = f(r)e iθ (44) ϕ r f(r) e iθ { x1 = r cos θ x 2 = r sin θ (45) n e inθ f(r) f(r) r 97
99 f(0) = 0 r = 0 0 ϕ r f(r) e iθ e iθ θ ϕ S 1 S 1 minimize θ linear e iθ 98
100 θ 2 r 2 θ 2 ansatz f f + 1 r f 1 ( ) r 2 f f f 2 + m2 λ = 0 (46) tanh mathematica tanh 99
101 ( r ϕ) 2 ( θ ϕ) 2 θ 1/r 2 ϕ θ ϕ e iθ θ 0 1/r 2 ϕ r r 1/r 2 r 1/r r log r ϕ φ φ φ(x) ϕ couple ϕ µ ϕ φ µ ϕ(x) µ ϕ(x) iea µ (x)ϕ(x) (47) 100
102 A µ (x) A µ (x) A µ (x) + µ φ (48) combination D µ ϕ φ φ(x) A µ (x) A µ (x) ϕ 4 couple couple 101
103 propagate ( 1 S = d 3 x 4 F µνf µν + 1 ) 2 (D µϕ) D µ ϕ + V (ϕ) ϕ 4 ( θ ϕ) 2 ( θ ia θ )ϕ θ A θ A θ boundary condition φ A θ A θ r 0 (49) 102
104 A θ 0 A θ θ r 0 θ A θ r 0 A θ r A θ r F 12 nonzero F 12 F rθ rθ A θ r A θ r 103
105 A θ r r 0 r nonzero F 12 x 3 3- nonzero 104
106
107 Z µ Z µ massless Z µ Z µ ϕ ϕ ϕ kinetic term ϕ ϕ = m λ A µ mass term Z µ Z µ ϕ LHC ϕ (Higgs) Z µ ϕ Z Z fluctuation δϕ 106
108 ϕ 107
109 QCD QCD electric-magnetic duality dual Meissner effect 108
110 QCD ( ) mass finite ( ) 1/r log r log r = 0 r ϕ A µ log r ϕ log r consistent particle 109
111 3.4 ϕ magnetic monopole
112 ϕ ϕ 1, ϕ 2, ϕ 3 V (ϕ 1, ϕ 2, ϕ 3 ) = λ 4 ) 2 ((ϕ 1 ) 2 + (ϕ 2 ) 2 + (ϕ 3 ) 2 + m2 (50) λ m 2 S 1 S 2 3 S π 2 (S 2 ) = Z 111
113 ϕ ϕ(x) S 2 action 2 non-abelian 112
114 M
115 ϕ 1, ϕ 2, ϕ 3 M ϕ 1, ϕ 2, ϕ 3 M SO(3) SO(3) SO(3) M T M det M ϕ 1 + iϕ 2 e iϕ ϕ e iϕ 1 + iϕ M 1 + i 114
116 M M = 1 + iϵt M T T T T + T = 0, trt = 0 M real M T M = 1 det M = 1 T T T 1, T 2, T 3 M 1 M 2 M 2 M 1 exponential [T i, T j ] iϵ ijk T k couple W ±, Z 115
117 S 2 0 S 2 116
118 GUT W ± Z
119 118
120 coupling [GeV] anti- 119
121 g 1/e e g e g 120
122 D ( ) divergence 0 Maxwell ( ) divergence 0 ( ) 1 121
123 4 D 4.1 D ϕ 4 Einstein-Hilbert Maxwell g µν (x) 10 µ, ν 0 9 ( ) g µν η µν (x) 122
124 123
125 10 [17] 124
126 i E i = 0 E i exi r 3 r = 0 F i0 E i 0 A 0 = e r 125
127 Einstein-Hilbert Einstein Einstein matter ( g 00 = 1 2Gm ) r, g rr = ( 1 2Gm ) 1 (51) r g 00 A 0 1 r Schwarzschild g 00 1 r 126
128 r ±1 r 1 r r = 2Gm g 00 = 0 r Schwarzshild 127
129 128
130 2Gm 10 2 kg G G = [m 3 s 2 kg 1 ] Gm Gm 10 8 [m 3 s 2 ] 1 Gm c [m] Gm c 1[cm] 1cm 2 129
131 130
132 4.2 D D D D D *6 10 µ fix c µ X µ (τ, σ) σ 0 2π c µ 2 D *6 Polchinski Ref.[18] D 131
133 D D artificial 132
134 10 Neumann Dirichlet µ 0 p p p x i x i = c i D D Dirichlet D membrane Dirichlet Dirichlet D p D Dp Dp p p (pea) (brain) p p Dp 133
135 D D 10 A µ 10 µ D D x 0,, x p p + 1 A µ x 0 x 9 x 0 x p A µ µ µ 0 p p p Kaluza-Klein Kaluza-Klein reduction A µ 10 A µ p
136 A µ Φ i D Φ i Φ i Dp 10 Φ i ( p)φ 2 i = 0 i Dp X 4 X 4 4 i x 0 x 3 Φ x 0 x p 135
137 D D D D D D D D Dp p p p p 1 p 0 Polchinski [19] 136
138 Polchinski D D Polchinski D D D D D D 137
139 4.3 D D D D D Dp A µ Φ i x 0 x p Maxwell d p+1 x p + 1 Dp 138
140 D D D Dp σ = 0 2π A µ Φ i A (1,1) µ, A (2,1) µ, D 139
141 F µν F µν A µ 1, σ 1, σ 2, σ 3 140
142 [ 1 2 σ i, 1 2 σ j] = iϵ ijk 1 2 σ k SO(3) σ 1, σ 2, σ 3 D p + 1 SO(3) + Maxwell + D consistency [ 1 4 F µνf µν + ] D 1 1, ,
143 Φ i Φ i D Φ i A µ A µ Φ i 10 Dirichlet A µ Φ i Gauge-Higgs unification consistency D 142
144 143
145 5 D section section 2 elementary C 144
146 5.1 D contribute D D D D D large extra dimension model 10 [20] 145
147 m 1, m 2 1 r 2 1 r 1 r divergence 0 harmonic function r 1 r 1 r r 4 + n n+1 M pl(4+n) 4 + n n + 2 V (r) 1 1 r n+1 M pl(4+n) n + 2 n = 0 4 reduce 2 consistent n (extra dimension) Kaluza-Klein R 146
148 R r R 4 r R 4 1 r 1 r n+1 consistent V (r) = m 1m M pl(4+n) R n r 1 r n+1 1 R n 1 r r = R r 1 r 2 (52) M 2 pl = M n+2 pl(4+n) Rn (53) (52) 2 147
149 W weak 10 2 [GeV] [GeV] (53) M pl(4+n) weak M pl 10 3 [GeV] LHC M pl(4+n) M pl(4+n) 10 3 [GeV] (53) R R n 19 [m] (54) GeV 148
150 n = effective n = 1 R [m] n = r 10 3 [m] [22] * [m] 1[mm] 10 3 [m] 1[mm] *7 Extra Dimensions O(10 1 ) [mm] 149
151 1[mm] bound improve 1[mm] 1[mm] D D D D matter mm 150
152 drastic LHC LHC LHC LHC 10 2 [kg] 1[cm] Planck Planck 10 3 [GeV] Schwarzschild 151
153 Gm combination G Planck 10 3 [GeV] Planck 2 1 G 3 Schwarzschild Schawarzschild Schwarzschild 1[cm] 3 Schwarzschild LHC Schwarzschild Schwarzschild 152
154 153
155 matter Hawking Hawking [21] Hawking LHC Schwarzschild matter LHC Hawking Hawking Hawking Hawking Hawking 154
156 Hawking LHC ( ) ( ) ( ) ( ) assign ( ) D D ( ) D D matter D 155
157 Planck weak mm mm 10 4 [ev] M pl M pl 2 R 10 4 [ev] weak 1 - [23, 24] 1 n 1 x 4 x
158 5 5 g MN (x µ, x 4 ) = e 2kx4 e 2kx4 e 2kx4 e 2kx4 1 (55) x 4 1 x 0 x 3 x 4 exponential entry 5 Einstein 5 5 Einstein-Hilbert Kaluza-Klein - matter x 4 matter x 4 = const x 4 = const
159 x 4 = c matter Higgs S = d 4 x(dx 4 ) [ det(g) δ(x 4 1 c) 2 gmn M ϕ N ϕ 1 ) 2 ] (ϕ 4 λ 2 + m2 λ 2 (56) δ x 4 = c matter consistent contract volume δ δ localize 158
160 x 4 δ ϕ = ϕe kc ϕ canonical normalize 1/2 det(g) det(g) g MN ϕ 1/2 normalize 1/2 normalize potential term ϕ m2 λ factor ϕ = m λ e k ( ) factor factor warp factor warp exponential exponential exponential exponential k 1 c kc 10 exponential e kc factor ϕ weak Planck exponential 159
161 log exponential 2 D motivate matter
162 A µ D D D D 161
163 D x 1, x 2, x 3 x 4, x 5,, x 9 extra dimension S 1 Kaluza-Klein 3 shrink matter 3 2 singlet matter bifundamental bifundamental matter 2 ( (i) ) 3 ( (ii) ) 162
164 (i) (ii) (i) 2 (ii) 3 bifundamental 2 D D bifundamental matter matter bifundamental matter D 1 Higgs A,B,C 3 3 string string tension string 2 string sweep string 3 matter content D 5 consistent consistency 1 D ( ) - 2 warp factor suppress suppress ( ) confusing 1 1 matter matter matter matter Planck matter matter matter 163
165 Planck consistent ( ) Planck 10 3 [GeV] GUT [GeV] ( ) D GUT D matter GUT motivation SU(3), SU(2), U(1) coupling 1 coupling 3 motivation rank matter D matter D GUT coupling unification coupling 1 coupling coupling GUT coupling 1 matter GUT D GUT D GUT matter constraint ( ) D low energy effective theory matter ( ) ( p.124 D ) ( ) (RS ) ( ) extra dimension 4 ( ) D3 low energy theory Yang-Mills ( ) 164
166 D scalar Kaluza-Klein mode couple covariant (RS) fluctuation - 4 ( ) Yukawa D Yukawa ( ) D matter content naive matter Yukawa Yukawa *8 Yukawa *8 Ref.[25] 165
167 5.2 QCD QCD SU(3) 3 3 Yang-Mills QCD QCD QCD kinetic term commutator 166
168 167
169 2 3 SU(3) singlet singlet 3 3 singlet 3 3 singlet singlet Regge linear Regge trajectory J 2 QCD 168
170 mass string mass ( m 2 = 1 ls ) nn n (57) n>0 N n 0 tachyon 1 α n µ oscillator N = 1 N = 0 scalar N α µ µ µ m 2 Regge trajectory QCD picture 1 α QCD QCD 169
171 2 L L QCD 170
172 linear 1 L linear 171
173 / D / / D / / D D QCD / *9 / QCD section confirm string QCD / D3 D3 N D3 Dirichlet boundary condition SU(N) N N D *9 / Ref.[26] Ref.[27, 28] 172
174 equality D D QCD N = 3 QCD 10 equality 1 2 / statement 10 [29] 1 173
175 * [30, 31] constraint constraint constraint SU(N) N N NgY 2 M λ t Hooft coupling λ constraint constraint coupling constant N N SU(N) N coupling constant λ t Hooft N [34] *10 / [32, 33] 174
176 t Hooft t Hooft λ weak λ QCD QCD 10 N QCD N = 3 N = 3 N = n = 1 n = 2 n = n = 0, 1, statement statement N t Hooft N QCD SU(3) 3 N N spoil N QCD N = 3 QCD QCD N 175
177 3 10 g 00 g 99 0, 1, 2, R4 r r 3 4 x 4 R 3 D N D R 4 N g s l s N SU(N) D3 r 0 f(r) 1 R4 r f(r) 4 g 00 g 33 r2 R 2 g rr R2 r exponential 2 5 D
178 Planck l p 0 Planck 1 l s 1 α α l 2 s l s 0 2 Planck l p Planck 10 1 l = 1 1 p 2 gs 2 l s 8 (i) 3 R l s R R = (4πg s N) 1 4 l S g s gy 2 M open string coupling 2 closed string coupling NgY 2 M (= λ) 1 t Hooft coupling (ii) l p R l p R N
179 anti linear SU(3) 3 3 fundamental 3 D3 D3 string D3 string QCD SU(3) / D3 178
180 string bulk / [35, 36] 3 anti L 1 L 1 1 L SU(3) superpartner QCD QCD 179
181 D3 D4 x 4 D4 effective [37] Kaluza-Klein massless SUSY massless D4 4 anti V (L) L 180
182 / QCD string tension 1 α Regge Regge / N QCD 181
183 / [38, 39, 40, 41, 42] [43, 44] [45, 41] [46, 47] [48, 49, 50] [51, 52, 53] * 11 / SU(3) N N 3 1 N QCD map *11 Ref.[26] Ref.[54] [55] [41] AdS/CFT QGP Ref.[56] Ref.[57] AdS/CFT 182
184 6 D LHC 1 statement 5 ( ) D4 string tension ( ) 183
185 vector ρ mass 1 ( ) non-planar 1 N 90 2 ( ) pure Yang-Mills non-planar 1 N suppress N 1 N correction N 3 3 N 2 [1] P. Minkowski, Mu E Gamma At A Rate Of One Out Of 1-Billion Muon Decays?, Phys. Lett. B 67, 421 (1977). [2] T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, In Proceedings of the Workshop on the Baryon Number of the Universe and Unified Theories, Tsukuba, Japan, Feb 1979, edited by O. Sawada and A. Sugamoto (KEK ) [3] M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors And Unified Theories, in Supergravity, Proceedings of the Workshop, Stony Brook, NY, 1979, edited by P. van Nieuwenhuizen and D. Freedman (North-Holland, Amsterdam, 1979) [4] G. t Hooft and M. J. G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20, 69 (1974). [5] M. J. G. Veltman, Quantum Theory Of Gravitation, SPIRES entry In *Les Houches 1975, Proceedings, Methods In Field Theory*, Amsterdam 1976, [6] S. Deser and P. van Nieuwenhuizen, One Loop Divergences Of Quantized Einstein-Maxwell Fields, Phys. Rev. D 10, 401 (1974). [7] S. Deser, H. S. Tsao and P. van Nieuwenhuizen, One Loop Divergences Of The Einstein Yang-Mills System, Phys. Rev. D 10, 3337 (1974). [8] M. H. Goroff and A. Sagnotti, The Ultraviolet Behavior Of Einstein Gravity, Nucl. Phys. B 266, 709 (1986). [9] M. B. Green, J. H. Schwarz and E. Witten, SUPERSTRING THEORY. VOL. 1: INTRODUC- TION, Cambridge, Uk: Univ. Pr. (1987) 469 P. (Cambridge Monographs On Mathematical Physics) [10] J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge, UK: Univ. Pr. (1998) 402 P. [11] A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20, 5513 (2005) [arxiv:hep- 184
186 th/ ]. [12] S. Mandelstam, The n loop string amplitude: Explicit formulas, finiteness and absence of ambiguities, Phys. Lett. B 277, 82 (1992). [13] N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 0409, 047 (2004) [arxiv:hep-th/ ]. [14] N. Seiberg and E. Witten, Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory, Nucl. Phys. B 426, 19 (1994) [Erratum-ibid. B 430, 485 (1994)] [arxiv:hepth/ ]. [15] N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, Nucl. Phys. B 431, 484 (1994) [arxiv:hep-th/ ]. [16] R. F. Dashen, B. Hasslacher and A. Neveu, Nonperturbative Methods And Extended Hadron Models In Field Theory. 2. Two-Dimensional Models And Extended Hadrons, Phys. Rev. D 10, 4130 (1974). [17] G. T. Horowitz and A. Strominger, Black strings and P-branes, Nucl. Phys. B 360, 197 (1991). [18] J. Polchinski, Lectures on D-branes, arxiv:hep-th/ [19] J. Polchinski, Dirichlet-Branes and Ramond-Ramond Charges, Phys. Rev. Lett. 75, 4724 (1995) [arxiv:hep-th/ ]. [20] N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429, 263 (1998) [arxiv:hep-ph/ ]. [21] S. W. Hawking, Particle Creation By Black Holes, Commun. Math. Phys. 43, 199 (1975) [Erratumibid. 46, 206 (1976)]. [22] K. Nakamura et al. (Particle Data Group), Review of particle physics, J. Phys. G 37, (2010) [23] L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83, 3370 (1999) [arxiv:hep-ph/ ]. [24] L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83, 4690 (1999) [arxiv:hep-th/ ]. [25] T. Higaki, N. Kitazawa, T. Kobayashi and K. j. Takahashi, Flavor structure and coupling selection rule from intersecting D-branes, Phys. Rev. D 72, (2005) [arxiv:hep-th/ ]. [26] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323, 183 (2000) [arxiv:hep-th/ ]. [27] I. R. Klebanov, TASI lectures: Introduction to the AdS/CFT correspondence, arxiv:hepth/ [28] J. M. Maldacena, Lectures on AdS/CFT, arxiv:hep-th/ [29] J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arxiv:hep-th/ ]. [30] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428, 105 (1998) [arxiv:hep-th/ ]. [31] E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998) [arxiv:hepth/ ]. [32] G. t Hooft, Dimensional reduction in quantum gravity, arxiv:gr-qc/
187 [33] L. Susskind, The World As A Hologram, J. Math. Phys. 36, 6377 (1995) [arxiv:hep-th/ ]. [34] G. t Hooft, A PLANAR DIAGRAM THEORY FOR STRONG INTERACTIONS, Nucl. Phys. B 72, 461 (1974). [35] S. J. Rey and J. T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22, 379 (2001) [arxiv:hep-th/ ]. [36] J. M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80, 4859 (1998) [arxiv:hep-th/ ]. [37] E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998) [arxiv:hep-th/ ]. [38] M. Kruczenski, D. Mateos, R. C. Myers and D. J. Winters, Meson spectroscopy in AdS/CFT with flavour, JHEP 0307, 049 (2003) [arxiv:hep-th/ ]. [39] E. Witten, Baryons and branes in anti de Sitter space, JHEP 9807, 006 (1998) [arxiv:hepth/ ]. [40] D. J. Gross and H. Ooguri, Aspects of large N gauge theory dynamics as seen by string theory, Phys. Rev. D 58, (1998) [arxiv:hep-th/ ]. [41] T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113, 843 (2005) [arxiv:hep-th/ ]. [42] T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114, 1083 (2005) [arxiv:hep-th/ ]. [43] K. Hashimoto, Holographic Nuclei, Prog. Theor. Phys. 121, 241 (2009) [arxiv: [hep-th]]. [44] K. Hashimoto, T. Sakai and S. Sugimoto, Nuclear Force from String Theory, Prog. Theor. Phys. 122, 427 (2009) [arxiv: [hep-th]]. [45] J. Babington, J. Erdmenger, N. J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in non-supersymmetric gauge / gravity duals, Phys. Rev. D 69, (2004) [arxiv:hepth/ ]. [46] G. Policastro, D. T. Son and A. O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87, (2001) [arxiv:hep-th/ ]. [47] D. Teaney, Effect of shear viscosity on spectra, elliptic flow, and Hanbury Brown-Twiss radii, Phys. Rev. C 68, (2003) [arxiv:nucl-th/ ]. [48] C. P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L. G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 0607, 013 (2006) [arxiv:hep-th/ ]. [49] S. S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74, (2006) [arxiv:hep-th/ ]. [50] H. Liu, K. Rajagopal and U. A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett. 97, (2006) [arxiv:hep-ph/ ]. [51] C. Csaki, H. Ooguri, Y. Oz and J. Terning, Glueball mass spectrum from supergravity, JHEP 9901, 017 (1999) [arxiv:hep-th/ ]. [52] R. C. Brower, S. D. Mathur and C. I. Tan, Glueball Spectrum for QCD from AdS Supergravity Duality, Nucl. Phys. B 587, 249 (2000) [arxiv:hep-th/ ]. [53] K. Hashimoto, C. I. Tan and S. Terashima, Glueball Decay in Holographic QCD, Phys. Rev. D 77, (2008) [arxiv: [hep-th]]. [54] J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Eur. Phys. J. A 35, 81 (2008) [arxiv:
188 [hep-th]]. [55] A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 0206, 043 (2002) [arxiv:hepth/ ]. [56] D. T. Son and A. O. Starinets, Ann. Rev. Nucl. Part. Sci. 57, 95 (2007) [arxiv: [hep-th]]. [57] J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010, (2010) [arxiv: [hep-th]]. 187
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