A defect action for Wilson loops

Understand

An effective action is proposed to compute the expectation value of Wilson loops in $(S)U(N)$ gauge theories.

• The action consists of fermions localized on the loop and an Abelian gauge field that fixes the representation.
• The discussion is limited to weak coupling and Wilson loops in the fundamental representation extended along a smooth curve, but there are no restrictions on the matter content as long as the theory has a UV fixed point or it is conformal.
• For a circular Wilson loop it is found that the expectation value coincides at leading order with the exact result of the $1/2$ BPS Wilson loop of ${\cal N}=4$ super Yang-Mills, which is determined by a solvable Gaussian matrix model.