$\mathcal{N}=4$ line defect correlators of type BCD

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 $Ad{S}_2$ and those of the fat string, the D5-brane wrapping $Ad{S}_2$ $\times$ ${\mathbb{R}\mathbb{P}}^4$.