Wilson Loop Operators In AdS/CFT Duality

The thesis is about Wilson loop operators in AdS/CFT duality AdS/CFT is the first realization of holographic principle of quantum gravity,it also provides a powerful method to study strongly coupled gauge theory.Wilson loops are important nonlocal operators in gauge theory,by studying Wilson loops in the context of AdS/CFT duality we can gain deeper understanding of Wilson loops and AdS/CFT duality itself.The fist chapter includes some background information:Wilson loops in gauge theory,string picture of QCD,string theory and AdS/CFT duality.The second chapter study Wilson loop operators in AdS₅/CFT₄ duality,the match-ing between the two sides provides nontrivial check for AdS/CFT duality.The third chapter study Wilson surface operators in AdS₇/CFT₆ duality via M-theory branes.The last chapter summarizes the status of study of Wilson loop operators in AdS/CFT duality,and prospect further study.Our work focus on studying higher rank Wilson loops(surfaces)via D/M branes in AdS space:(1)We study higher rank Wilson-'t Hooft loop operator in N=4 SYM via D3 brahe in AdS₅×S⁵ with both electric and magnetic fields on its worldvolume.We obtain D3 brahe dual of 1/2 BPS Wilson-'t Hooft loop, its vacuum expectation value and SL(2,Z)duality.Our work generalize Wilson loop/D brahe duality,provides an example of studying nonperturbative proper-ties of gauge theory via AdS/CFT duality.(2)We study higher rank Wilson surface operators in 6 dimensional non-Abelian(0,2)SCFT via M5 branes in AdS₇×S⁴ spacetime.We find the corresponding M5 brahe configuration and ob-tain the vacuum expectation value of Wilson surfaces.Our results have similar properties with Abelian case and indicate it's reasonable to use M5 branes as the AdS dual of higher rank surface operators.