Advances in High Energy Physics

Review Article

On String Integrability: A Journey through the Two-Dimensional Hidden Symmetries in the AdS/CFT Dualities

Table 2

Summarized comparison between the two gauge/string dualities.
A d S 5 / C F T 4 A d S 4 / C F T 3
IIB on A d S 5 × S 5 AdS side IIA on A d S 4 × ℂ 𝑃 3
𝒩 = 4 SYM in 4d CFT side 𝒩 = 6 CS-matter in 3d
𝜆 = 𝑔 2 Y M 𝑁 ’t Hooft coupling 𝜆 = 𝑁 / 𝑘
𝑇 = 𝑅 2 / 2 𝜋 𝛼 = √ 𝜆 / 2 𝜋 String tension 𝑇 = 𝑅 2 / 2 𝜋 𝛼 = 2 5 / 2 𝜋 √ 𝜆
𝑔 𝑠 = 𝑔 2 Y M / 4 𝜋 String coupling 𝑔 𝑠 = ( 3 2 𝜋 2 ( 𝑁 / 𝑘 5 ) ) 1 / 4
S U ( 𝑁 ) gauge group U ( 𝑁 ) 𝑘 × U ( 𝑁 ) − 𝑘
P S U ( 2 , 2 ∣ 4 ) global symmetry O S p ( 6 ∣ 4 )
A d S 5 × S 5 = ( S O ( 4 , 2 ) / S O ( 4 , 1 ) ) × ( S O ( 6 ) / S O ( 5 ) ) bosonic subgroup A d S 4 × ℂ 𝑃 3 = ( S O ( 3 , 2 ) / S O ( 3 , 1 ) ) × ( S U ( 4 ) / U ( 3 ) )