Gauge/gravity duality: an overview Z. Bajnok
Gauge/gravity duality: an overview Z. Bajnok
Gauge/gravity duality: an overview Z. Bajnok
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R 2<br />
α ′<br />
II B superstring on AdS 5 × S 5<br />
4D<br />
Minkowski<br />
space<br />
5D<br />
<strong>an</strong>ti de Sitter<br />
space<br />
AdS/CFT correspondence (Maldacena 1998)<br />
5D sphere<br />
≡<br />
space<br />
time<br />
extra dimension<br />
( )<br />
∂a X M ∂ a X M + ∂ a Y M ∂ a Y M + . . .<br />
∑ 6<br />
1 Y i 2 = R 2 − + + + +− = −R 2<br />
∫ dτdσ<br />
4π<br />
Couplings: √ λ = R2<br />
α ′ , g s = λ N → 0<br />
2D QFT<br />
String energy levels: E(λ)<br />
E(λ) = E(∞) + √ E 1<br />
+ E 2<br />
λ λ + . . .<br />
Dictionary<br />
2<br />
g 2 Y M<br />
strong↔weak<br />
⇓<br />
N = 4 D=4 SU(N) SYM<br />
∫ d 4 xTr [ − 1 4 F 2 − 1 2 (DΦ)2 + iΨD/ Ψ + V ]<br />
V (Φ, Ψ) = 1 4 [Φ, Φ]2 + Ψ[Φ, Ψ]<br />
P SU(2,2|4)<br />
β = 0 superconformal<br />
SO(5)×SO(1,4)<br />
gaugeinvari<strong>an</strong>ts:O = Tr(Φ 2 ), det( )<br />
λ = gY 2 MN , N → ∞ pl<strong>an</strong>ar limit<br />
〈O n (x)O m (0)〉 = δ nm<br />
|x| 2∆ n(λ)<br />
Anomalous dim ∆(λ)<br />
∆(λ) = ∆(0) + λ∆ 1 + λ 2 ∆ 2 + . . .<br />
2D integrable QFT<br />
√<br />
spectrum: Q = 1, 2, . . . , ∞ dispersion: ɛ Q (p) = Q 2 + λ π 2 sin2 p<br />
2<br />
Exact scattering matrix: S Q1 Q 2<br />
(p 1 , p 2 , λ)
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