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

Table 1

Summary of the contents and parameters involved in AdS₅/CFT₄ duality.

Gauge theory		String theory
Yang Mills coupling 𝑔YM		String coupling 𝑔𝑠
Number of colors 𝑁		String tension 𝑇≡𝑅^2/2𝜋𝛼^
’t Hooft coupling 𝜆≡𝑔^2YM𝑁		AdS5×S^5 radius R
	AdS5/CFT4
	𝑔𝑠=𝑔^2YM/4𝜋
	𝑇=√𝜆/2𝜋
	’t Hooft limit
𝑁→∞ 𝜆=fixed		𝑔𝑠→0 𝑇=fixed
planar limit		noninteracting string
	Strong Coupling
𝑁→∞ 𝜆≫1		𝑔𝑠→0 𝑇≫1
		classical supergravity
	Weak coupling
𝑁→∞ 𝜆≪1		𝑔𝑠→0𝑇≪1
perturbative SYM