Boundary Wilson and 't Hooft line two-point functions in N=4 SYM match exactly under S-duality, with closed forms from Macdonald polynomials.
$\mathcal{N}=4$ line defect correlators of type BCD
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abstract
We analyze the line defect correlation functions decorating the supersymmetric indices of $\mathcal{N}=4$ super Yang-Mills theories with orthogonal and symplectic gauge groups. We obtain exact closed-form expressions for the correlators by means of combinatorial methods associated with the group characters, including the generalized Murnaghan-Nakayama rules. The exact results for the large $N$ correlators lead to the gravity indices for the gravity dual spectrum of the fluctuations of the fundamental string wrapping $AdS_2$ and those of the fat string, the D5-brane wrapping $AdS_2$ $\times$ $\mathbb{RP}^4$.
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S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
Boundary Wilson and 't Hooft line two-point functions in N=4 SYM match exactly under S-duality, with closed forms from Macdonald polynomials.