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I know that for a Wilson loop, in the fundamental representation, the dual is a string worldsheet ending on the loop at the boundary of AdS. Similarly, I guess that the object corresponding to ’t Hooft loop will be a D-string worldsheet.

There are some papers calculating the ’t Hooft loop in a high-dimensional representation, like this

https://arxiv.org/abs/hep-th/0501109

but I cannot find any paper on the fundamental representation, which I guess it will be a D1-brane ending on the loop, or something like that.

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